Exhibit 5.1

[Wachtell, Lipton, Rosen & Katz Letterhead]

July 26, 2018

M&T Bank Corporation

One M&T Plaza

Buffalo, New York 14203

Ladies and Gentlemen:

We have acted as special counsel to M&T Bank Corporation (the “Company”), a New York corporation, in connection with the offer and sale (the “Offering”) by the Company of $500,000,000 aggregate principal amount of its 3.550% Fixed Rate Senior Notes due 2023 and $250,000,000 aggregate principal amount of its Floating Rate Senior Notes due 2023 (collectively, the “Notes”) pursuant to the Underwriting Agreement, dated July 19, 2018 (the “Underwriting Agreement”), among the Company, Morgan Stanley & Co. LLC, Credit Suisse Securities (USA) LLC, J.P. Morgan Securities LLC and UBS Securities LLC, as representatives of the several underwriters listed on Schedule A attached thereto (the “Underwriters”). The Notes are being offered and sold under a registration statement on Form S-3ASR under the Securities Act of 1933, as amended (the “Securities Act”), filed with the Securities and Exchange Commission (the “Commission”) on September 18, 2015 (File No. 333-207030) (the “Registration Statement”), including a base prospectus dated September 18, 2015, and a prospectus supplement dated July 19, 2018 (the “Prospectus Supplement”).

The Notes were issued under the Indenture, dated as of May 24, 2007 (the “Base Indenture”), between the Company and The Bank of new York, as trustee (the “Trustee”), as supplemented by the Second Supplemental Indenture, dated as of July 26, 2017 (the “Supplemental Indenture” and, together with the Base Indenture, the “Indenture”), between the Company and The Bank of New York Mellon, as Trustee. The Supplemental Indenture and the form of Notes are filed as exhibits to the Company’s Current Report on Form 8-K dated the date hereof (the “Form 8-K”).

M&T Bank Corporation

July 26, 2018

Page 2

In rendering this opinion to the Company, we have examined such corporate records and other documents, and we have reviewed such matters of law, as we have deemed necessary or appropriate, including the Underwriting Agreement, the Indenture and the Notes, which we refer to herein as the “Transaction Documents”. In rendering this opinion, we have, with your consent, relied upon oral and written representations of officers of the Company and certificates of officers of the Company and public officials with respect to the accuracy of the factual matters addressed in such representations and certificates. In addition, in rendering this opinion we have, with your consent, assumed the genuineness of all signatures or instruments relied upon by us, and the conformity of certified copies submitted to us with the original documents to which such certified copies relate. We have also assumed the valid authorization, execution and delivery of each of the Transaction Documents by each party thereto other than the Company, and we have assumed that each such other party (in the case of parties which are not natural persons) has been duly organized and is validly existing and in good standing under its jurisdiction of organization, that each such other party has the legal capacity, power and authority to perform its obligations thereunder and that each of the Transaction Documents constitutes the valid and binding obligation of all such other parties, enforceable against them in accordance with its terms.

Based on the foregoing, and subject to the qualifications and limitations stated herein, we are of the opinion that the Notes, when authenticated by the Trustee in the manner provided in the Indenture and issued and delivered against payment of the purchase price therefor, will be valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

The opinion set forth above is subject to the effects of (a) bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting the enforcement of creditors’ rights generally, (b) general equitable principles (whether considered in a proceeding in equity or at law) and (c) an implied covenant of good faith and fair dealing, (d) provisions of law that require that a judgment for money damages rendered by a court in the United States be expressed only in United States dollars, (e) limitations by any governmental authority that limit, delay or prohibit the making of payments outside the United States and (f) generally applicable laws that (i) provide for the enforcement of oral waivers or modifications where a material change of position in reliance thereon has occurred or provide that a course of performance may operate as a waiver, (ii) limit the availability of a remedy under certain circumstances where another remedy has been elected, (iii) limit the enforceability of provisions releasing, exculpating or exempting a party from, or requiring indemnification or contribution of a party for, liability for its own action or inaction, to the extent the action or inaction involves negligence, gross negligence, recklessness, willful misconduct or unlawful conduct, (iv) may, where less than all of a contract may be unenforceable, limit the enforceability of the balance of the contract to circumstances in which the unenforceable portion is not an essential part of the agreed exchange, (v) may limit the enforceability of provisions providing for compounded interest, imposing increased interest rates or late payment charges upon delinquency in payment or default or providing for liquidated damages or for premiums or penalties upon acceleration or (vi) limit the waiver of rights under usury laws. We express no

M&T Bank Corporation

July 26, 2018

Page 3

opinion as to whether, or the extent to which, the laws of any particular jurisdiction apply to the subject matter hereof, including, without limitation, the enforceability of the governing law provision contained in the Notes or the Indenture. Furthermore, the manner in which any particular issue relating to the opinions would be treated in any actual court case would depend in part on facts and circumstances particular to the case and would also depend on how the court involved chose to exercise the wide discretionary authority generally available to it. We express no opinion as to the effect of Section 210(p) of the Dodd-Frank Wall Street Reform and Consumer Protection Act.

This opinion is given on the basis of the statutory laws and judicial decisions in effect, and the facts existing, as of the date hereof. We have not undertaken any obligation to advise you of changes in matters of fact or law which may occur, and we do not opine with respect to any law, regulation, rule or governmental policy which may be enacted or adopted, after the date hereof. This opinion speaks as of its date, and we undertake no (and hereby disclaim any) obligation to update this opinion.

We are members of the Bar of the State of New York, and we have not considered, and we express no opinion as to, the laws of any jurisdiction other than the laws of the State of New York and the federal laws of the United States of America, in each case as in effect on the date hereof.

We hereby consent to the filing of this opinion with the Commission as an Exhibit to the Company’s Current Report on Form 8-K filed on July 26, 2018. We also consent to the reference to our firm under the caption “Validity of Securities” in the Prospectus Supplement constituting a part of the Registration Statement. In giving this consent, we do not thereby admit that we are experts within the meaning of Section 11 of the Securities Act or included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

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Very truly yours,

/s/ Wachtell, Lipton, Rosen & Katz