Exhibit 5.1

May 29, 2015

Celsion Corporation

997 Lenox Drive, Suite 100

Lawrenceville, NJ 08648

Ladies and Gentlemen:

We refer to the Registration Statement on Form S-3, File No. 333-183286, as amended by Amendment No. 1 thereto (the “Registration Statement”), filed by Celsion Corporation, a Delaware corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), which Registration Statement was declared effective by the Commission on September 14, 2012 under the Securities Act. Pursuant to the Registration Statement, the Company is issuing 3,000,000 shares (the “Shares”) of the Company’s common stock, par value $0.01 per share. The Shares are to be sold by the Company pursuant to a Securities Purchase Agreement dated May 27, 2015 (the “Purchase Agreement”), among the Company and the purchasers named therein.

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

In rendering the opinion set forth in this letter, we have examined and relied upon copies of the Registration Statement, the Company’s base prospectus dated September 14, 2012 (the “Base Prospectus”), the Company’s prospectus supplement dated May 27, 2015 supplementing the Base Prospectus and relating to the Shares (the “Prospectus Supplement”), the Purchase Agreement, the Company’s certificate of incorporation and bylaws, each as currently in effect, and the resolutions adopted by the board of directors of the Company relating to the Registration Statement and the issuance of the Shares by the Company. We have also examined originals, or copies of originals certified to our satisfaction, of such agreements, documents, certificates and statements of the Company and other corporate documents and instruments, and have examined such questions of law, as we have considered relevant and necessary as a basis for this opinion letter. We have assumed the authenticity of all documents submitted to us as originals, the genuineness of all signatures, the legal capacity of all persons and the conformity with the original documents of any copies thereof submitted to us for examination. As to facts relevant to the opinions expressed herein, we have relied without independent investigation or verification upon, and assumed the accuracy and completeness of, certificates, letters and oral and written statements and representations of public officials and officers and other representatives of the Company.

Celsion Corporation

May 29, 2015

Page 2

Based on and subject to the foregoing and the other limitations, qualifications and assumptions set forth herein, we are of the opinion that the issuance and sale of the Shares covered by the Registration Statement pursuant to the Purchase Agreement have been duly authorized by the Company, and such Shares will be validly issued, fully paid and non-assessable when certificates representing such Shares shall have been duly executed, countersigned and registered and duly delivered to the purchasers thereof against payment of the agreed consideration therefor in an amount not less than the par value thereof or, if any such Shares are to be issued in uncertificated form, the Company’s books shall reflect the issuance of such Shares to the purchasers thereof against payment of the agreed consideration therefor in an amount not less than the par value thereof, in accordance with the Purchase Agreement.

This opinion letter is limited to the General Corporation Law of the State of Delaware. We express no opinion as to the laws, rules or regulations of any other jurisdiction, including, without limitation, the federal laws of the United States of America or any state securities or blue sky laws.

We hereby consent to the filing of this opinion letter as an exhibit to the Company’s Current Report on Form 8-K to be filed with the Commission on the date hereof, which Form 8-K will be incorporated by reference into the Registration Statement, and to the reference to our Firm under the caption “Legal Matters” in the Prospectus Supplement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Sidley Austin LLP