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

Telefónica, S.A.

TABLE OF CONTENTS

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

As far as the resolution of a reduction in share capital adopted by the Annual General Shareholders’ Meeting of TELEFÓNICA, S.A., held on May 12, 2016, (cancellation of shares of the Company’s own stock, subject to effective receipt of the proceeds from the closing of the sale of Telefónica’s operations in O2 UK), the Board of Directors of the Company has decided, at its meeting held today, to waive the condition precedent established by said resolution, and consequently, proceed to carry out the corresponding share capital reduction, by means of the cancellation of 74,627,988 shares of the Company’s own stock, which represent, approximately, 1.5% of the Company’s current share capital.

In the following days, the appropriate requirements for said execution will be carried out, and such execution will be announced through the corresponding significant event.

Madrid, September 28, 2016

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.