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FORM 6-K

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

Report of Foreign Private Issuer

Pursuant to Rule 13a-16 or 15d-16

of the Securities Exchange Act of 1934

For the month of September, 2016

Commission File Number: 001-09531

Telefónica, S.A.

(Translation of registrant’s name into English)

Distrito Telefónica, Ronda de la Comunicación s/n,

28050 Madrid, Spain

3491-482 87 00

(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F:

Form 20-F  x            Form 40-F  ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1):

Yes  ¨            No   x

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7):

Yes  ¨            No   x

Indicate by check mark whether by furnishing the information contained in this Form, the registrant is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934:

Yes  ¨            No   x

If “Yes” is marked, indicate below the file number assigned to the registrant in connection with Rule 12g3-2(b): N/A

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Telefónica, S.A.

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RAMIRO SÁNCHEZ DE LERÍN GARCÍA-OVIES

General Secretary and

Secretary to the Board of Directors

TELEFÓNICA, S.A.

TELEFÓNICA, S.A. as provided in article 228 of the Spanish Securities Market Act (Ley del Mercado de Valores), hereby reports the following

SIGNIFICANT EVENT

Telefónica, S.A. announces its intention to proceed with an offering (the “Offering”) of shares of its telecommunications infrastructure subsidiary Telxius Telecom, S.A.U. (“Telxius”), addressed to qualified investors. The Offering is expected to take place during the second half of 2016, following receipt of the approval by the Comisión Nacional del Mercado de Valores of the Offering prospectus.

Telxius intends to apply for the listing of its shares on the Barcelona, Bilbao, Madrid and Valencia stock exchanges, as well as their inclusion in the Spanish electronic trading system (Continuous Market).

The free float of Telxius will be at least of 25%, the minimum legally required for the listing, and, at the same time, will enable Telefónica, S.A. to maintain a majority stake in Telxius immediately after the Offering.

In Madrid, 5 September 2016.

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IMPORTANT INFORMATION

This announcement is an advertisement and does not constitute an offering memorandum and nothing herein contains an offering of securities. No one should purchase or subscribe for any shares (the “Shares”) in Telxius Telecom, S.A.U. (“Telxius” the “Company”, and together with its subsidiaries, the “Group”) except on the basis of information contained in any prospectus published by the Company in connection with its initial public offering. The intended admission to listing of the Shares on the Barcelona, Bilbao, Madrid and Valencia stock exchanges and inclusion in the Spanish electronic trading system (Continuous Market) requires the approval by the Comisión Nacional de Mercado de Valores (the “CNMV”) of a prospectus (the “Prospectus”). Once approved, the Prospectus will be published and made available at the website of the CNMV (www.cnmv.es) and on Telxius’ website at www.telxius.com.

Neither Telefónica, S.A. nor the Company intends to register any securities referred to herein under the U.S. Securities Act of 1933, as amended (the “Securities Act”), and any such securities may not be offered or sold in the United States absent registration under the Securities Act or an available exemption from it. Neither this announcement nor any copy of it may be taken or transmitted into or distributed in Australia, Canada or Japan or any other jurisdiction which prohibits the same or to any securities analyst or other person in any of those jurisdictions. Any failure to comply with this restriction may constitute a violation of the securities laws of those countries.

This announcement is only addressed to and directed at persons in member states of the European Economic Area who are “qualified investors” within the meaning of Article 2(1)(e) of the Prospectus Directive (Directive 2003/71/EC, as amended by Directive 2010/73/EU to the extent implemented in the relevant member state). In addition, in the United Kingdom, this announcement is being distributed only to, and is directed only at, persons (i) having professional experience in matters relating to investments so as to qualify them as —investment professionals|| under Article 19(5) of the Financial Services and Markets Act 2000 (Financial Promotion) Order 2005; (ii) falling within Article 49(2)(a) to (d) of the Order; and/or (iii) to whom it may otherwise lawfully be communicated (all such persons referred to in (i), (ii) and (iii) together being —Relevant Persons||). This document must not be acted on or relied on (i) in the United Kingdom, by persons who are not Relevant Persons, and (ii) in any member state of the European Economic Area other than the United Kingdom, by persons who are not Qualified Investors.

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SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.