Exhibit 5.1

February 17, 2015

Delcath Systems, Inc.

1301 Avenue of the Americas

43rd Floor

New York, New York 10019

Ladies and Gentlemen:

We have acted as special counsel to Delcath Systems, Inc., a Delaware corporation (the “Company”), in connection with the Company’s sale of 2,460,000 shares (the “Shares”) of the Company’s Common Stock, par value $0.01 per share (the “Common Stock”), and warrants (the “Warrants”) to initially purchase up to an aggregate of 1,107,000 shares (the “Warrant Shares”) of Common Stock, pursuant to the Underwriting Agreement, dated February 11, 2015, by and among Roth Capital Partners, LLC, as the underwriter, and the Company (the “Underwriting Agreement”). The Shares and the Warrant Shares are referred to herein as the “Equity Securities” and the Warrants and the Equity Securities are referred to herein as the “Securities.” The terms of the Warrants are set forth in warrant agreements substantially in the form included as Exhibit A to the Underwriting Agreement (each signed warrant agreement, a “Warrant Agreement” and collectively the “Warrant Agreements”). The Securities were registered by the Company with the Securities and Exchange Commission (the “Commission”) on the shelf registration statement on Form S-3 (No. 333-183675) filed on August 31, 2012 by the Company with the Commission pursuant to the Securities Act of 1933, as amended (the “Securities Act”) and declared effective on October 9, 2012 (the “Registration Statement”), including the base prospectus, dated October 9, 2012, as supplemented by a prospectus supplement, dated February 11, 2015, filed by the Company with the Commission pursuant to Rule 424(b) (such prospectus supplement together with such base prospectus, the “Prospectus”) of the General Rules and Regulations under the Securities Act (the “Rules and Regulations”). The Registration Statement relates to, among other things, the issuance and sale by the Company, from time to time pursuant to Rule 415 of the Rules and Regulations, of $100,000,000 of various securities of the Company, including Common Stock and warrants.

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

Delcath Systems, Inc.

February 17, 2015

Page 2

In rendering the opinions stated herein, we have examined and relied upon the following:

(i) the Registration Statement;

(ii) the Amended and Restated Certificate of Incorporation of the Company, as certified by the Secretary of the State of Delaware and as certified by the Secretary of the Company (the “Certificate of Incorporation”);

(iii) the Amended and Restated By-laws of the Company, as currently in effect and as certified by the Secretary of the Company;

(iv) a copy of certain resolutions of the board of directors of the Company (the “Board of Directors”), adopted on February 3, 2015, relating to the sale of the Securities, as certified by the Secretary of the Company (the “Board Resolutions”);

(v) a copy of certain resolutions of the Deal Committee of the Board of Directors (the “Deal Committee”), adopted on February 11, 2015, relating to the sale of the Securities, as certified by the Secretary of the Company (the “Deal Committee Resolutions”); and

(vi) the Warrant Agreements.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents as we have deemed necessary or appropriate as a basis for the opinions stated below.

In our examination, we have assumed the genuineness of all signatures, including endorsements, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as facsimile, electronic, certified, conformed or photostatic copies and the authenticity of the originals of such copies. In making our examination of executed documents or documents to be executed, we have assumed that the parties thereto, other than the Company, will have been duly organized and be validly existing in good standing, had or will have the power, corporate or otherwise, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and the execution and delivery by such parties of such documents, and, as to parties other than the Company, the validity and binding effect thereof on such parties. In addition, we have assumed that the issuance and sale of the Securities do not, violate, conflict with or constitute a default under (i) any agreement or instrument to which the Company is subject (other than the Underwriting Agreement or the Warrant Agreements), (ii) any law, rule or regulation to which the Company is subject (other than Opined on Law, as defined below), (iii) any judicial or regulatory order or decree of any governmental authority (other than those under Opined on Law) or (iv) any

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February 17, 2015

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consent, approval, license, authorization or validation of, or filing, recording or registration with, any governmental authority (other than those under Opined on Law). As to any facts relevant to the opinions stated herein that we did not independently establish or verify, we have relied upon oral or written statements and representations of officers and other representatives of the Company and others and of public officials. We have also assumed that, upon issuance of any Equity Securities subsequent to the date hereof, the total number of shares of Common Stock of the Company issued and outstanding will not, after giving effect to the issuance of such Equity Securities, exceed the total number of shares of Common Stock that the Company is authorized to issue under its Certificate of Incorporation in effect at such time.

We do not express any opinion with respect to the laws of any jurisdiction other than (i) the General Corporations Law of the State of Delaware (the “DGCL”) and (ii) the laws of the State of New York, and to the extent that judicial or regulatory orders or decrees or consents, approvals, licenses, authorizations, validations, filings, recordings or registrations with governmental authorities are relevant, to those required under such laws (all of the foregoing being referred to as “Opined on Law”). We do not express any opinion with respect to the laws of any jurisdiction other than Opined on Law or as to the effect of any non-Opined on Law on the opinions stated herein.

The Underwriting Agreement and the Warrant Agreements are referred to herein as the “Transaction Agreements.”

The opinions stated herein are subject to the following qualifications:

(a) the opinions stated herein are limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer, preference and other similar laws affecting creditors’ rights generally, and by general principles of equity (regardless of whether enforcement is sought in equity or at law);

(b) except to the extent expressly stated in the opinions contained herein, we do not express any opinion with respect to the effect on the opinions stated herein of (i) the compliance or non-compliance of any party to any of the Transaction Agreements with any laws, rules or regulations applicable to such party or (ii) the legal status or legal capacity of any party to any of the Transaction Agreements;

(c) except to the extent expressly stated in the opinions contained herein, we do not express any opinion with respect to any law, rule or regulation that is applicable to any party to any of the Transaction Agreements or the transactions contemplated thereby solely because such law, rule or regulation is part of a regulatory regime applicable to any such party or any of its affiliates as a result of the specific assets or business operations of such party or such affiliates;

(d) we do not express any opinion with respect to any securities, antifraud, derivatives or commodities laws, rules or regulations or Regulations T, U or X of the Board of Governors of the Federal Reserve System;

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February 17, 2015

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(e) except to the extent expressly stated in the opinions contained herein, neither the execution and delivery by the Company of the Transaction Agreements nor the enforceability of each of the Transaction Agreements against the Company requires or will require the consent, approval, licensing or authorization of, or any filing, recording or registration with, any governmental authority under any law, rule or regulation of any jurisdiction;

(f) to the extent that any opinion relates to the enforceability of the choice of New York law and choice of New York forum provisions contained in any Transaction Agreement, the opinions stated herein are subject to the qualification that such enforceability may be subject to, in each case, (i) the exceptions and limitations in New York General Obligations Law sections 5-1401 and 5-1402 and (ii) principles of comity or constitutionality; and

(g) in rendering the opinion set forth in paragraph 3 below, we have assumed that the Exercise Price (as defined in the Warrant Agreements) will be at least equal to the par value of the Warrant Shares at the time of exercise.

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that:

We hereby consent to the filing of this opinion with the Commission. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable laws.