Exhibit 5.1

February 4, 2014

Fluidigm Corporation

7000 Shoreline Court, Suite 100

South San Francisco, California 94080

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to Fluidigm Corporation, a Delaware corporation (the “Company”), in connection with the filing by the Company with the Securities and Exchange Commission (the “Commission”) on January 29, 2014 of a registration statement on Form S-3 (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Act”), that became automatically effective under the Act pursuant to Rule 462(e) promulgated thereunder. The Registration Statement relates to the proposed offer, issuance and sale by the Company, from time to time pursuant to Rule 415 under the Act as set forth in the Registration Statement, the prospectus contained therein (the “Prospectus”) and the supplements to the prospectus referred to therein (the “Prospectus Supplements”) of up to an aggregate offering price of $350,000,00, or the equivalent thereof, of (a) shares of the Company’s common stock, $0.001 par value per share (the “Common Stock”), (b) shares of the Company’s preferred stock, $0.001 par value per share (the “Preferred Stock”), (c) the Company’s senior and subordinated debt securities (the “Debt Securities”), (d) warrants to purchase shares of the Company’s Common Stock, Preferred Stock or Debt Securities (the “Warrants”), or (e) units (the “Units”) consisting of Common Stock, Preferred Stock, Debt Securities, Warrants or any combination of the foregoing (the Common Stock, Preferred Stock, Debt Securities, Warrants and Units are collectively referred to herein as the “Company Securities.”

Pursuant to the Registration Statement, the Company has issued $201,250,000 of 2.75% Convertible Senior Notes due 2034 (the “Notes”), all of which will be sold to Piper Jaffray & Co. (the “Underwriter”), pursuant to that certain Underwriting Agreement, dated as of January 29, 2014 (the “Underwriting Agreement”), by and between the Company and the Underwriter.

The Notes have been issued in the form set forth in the Indenture, dated as of February 4, 2014 (the “Base Indenture”), by and between the Company and U.S. Bank National Association, as trustee (the “Trustee”), as amended and supplemented by the First Supplemental Indenture, dated as of February 4 2014 (the “First Supplemental Indenture,” as such First Supplemental Indenture amends and supplements the Base Indenture, the “Indenture”), by and between the Company and the Trustee. The Notes are also convertible initially up to 3,597,604 shares of Common Stock (such number of shares of Common Stock issuable upon conversion of the Notes referred to herein as, the “Conversion Shares”).

We have examined the Registration Statement, together with the exhibits thereto and the documents incorporated by reference therein; the base prospectus, dated January 29, 2014, together with the documents incorporated by reference therein, filed with the Registration Statement (the “Base Prospectus”); the preliminary prospectus supplement, dated January 29, 2013, in the form filed with the Commission pursuant to Rule 424(b) of the Securities Act; the final prospectus supplement, dated January 29, 2014, in the form filed with the Commission pursuant to Rule 424(b) of the Securities Act (collectively with the Base Prospectus, the “Prospectus Supplement”); the Indenture; and the Notes. In addition, we have examined such other instruments, documents, certificates and records which we have deemed relevant and necessary for the basis of our opinion hereinafter expressed.

Fluidigm Corporation

February 4, 2014

Page 2 of 3

In such examination, we have assumed: (i) the authenticity of original documents and the genuineness of all signatures; (ii) the conformity to the originals of all documents submitted to us as copies; (iii) the truth, accuracy and completeness of the information, representations and warranties contained in the instruments, documents, certificates and records we have reviewed; (iv) the Underwriting Agreement has been duly authorized and validly executed and delivered by the parties thereto (other than the Company); and (v) the legal capacity of all natural persons. As to any facts material to the opinions expressed herein that were not independently established or verified, we have relied upon oral or written statements and representations of officers and other representatives of the Company.

We express no opinion as to the laws of any jurisdiction, other than the federal laws of the United States of America, the laws of the State of New York and the laws of the State of Delaware, as such are in effect on the date hereof, and we have made no inquiry into, and we express no opinion as to, the statutes, regulations, treaties, common laws or other laws of any other nation, state or jurisdiction.

We express no opinion as to (i) the effect of any bankruptcy, insolvency, reorganization, arrangement, fraudulent conveyance, moratorium or other similar laws relating to or affecting the rights of creditors generally, (ii) rights to indemnification and contribution which may be limited by applicable law or equitable principles, or (iii) the effect of general principles of equity, including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing, the effect of judicial discretion and the possible unavailability of specific performance, injunctive relief or other equitable relief, and the limitations on rights of acceleration, whether considered in a proceeding in equity or at law.

Based on such examination, we are of the opinion that:

1. The Notes have been validly issued and constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

2. When the applicable conversion right has been duly exercised in accordance with the terms of the Notes and the Indenture, and the Conversion Shares have been issued and delivered upon such exercise in accordance with the terms of the Notes and the Indenture, the Conversion Shares will be validly issued, fully paid and nonassessable.

We hereby consent to the filing of this opinion as an exhibit to the Company’s Current Report on Form 8-K, filed on February 4, 2014, for incorporation by reference in the above-referenced Registration Statement and to the use of our name wherever it appears in the Registration Statement, the Base Prospectus, the Prospectus Supplement, and in any amendment or supplement thereto. In giving such consent, we do not believe that we are “experts” within the meaning of such term as used in the Act or the rules and regulations of the Commission issued thereunder with respect to any part of the Registration Statement, including this opinion as an exhibit or otherwise.

Fluidigm Corporation

February 4, 2014

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Very truly yours,

WILSON SONSINI GOODRICH & ROSATI

Professional Corporation

/s/ Wilson Sonsini Goodrich & Rosati, P.C.