UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 6-K

REPORT OF FOREIGN ISSUER

PURSUANT TO RULE 13a-16 OR 15d-16

UNDER THE SECURITIES EXCHANGE ACT OF 1934

For the month of December, 2013

Commission file number: 1-10110

BANCO BILBAO VIZCAYA ARGENTARIA, S.A.

(Exact name of Registrant as specified in its charter)

BANK BILBAO VIZCAYA ARGENTARIA, S.A.

(Translation of Registrant’s name into English)

Paseo de la Castellana, 81

28046 Madrid

Spain

(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

Banco Bilbao Vizcaya Argentaria, S.A. (“BBVA”), in compliance with the Securities Market legislation, hereby communicates the following

RELEVANT INFORMATION

Further to the relevant information disclosed by BBVA to the markets on July 20, 2013, and once the necessary authorisations have been obtained, BBVA announces that is has completed the sale of the entirety of its approximately 98.92% direct and indirect interest in Banco Bilbao Vizcaya Argentaria (Panamá), S.A. (“BBVA Panamá”) to Leasing Bogotá, S.A., Panamá, a subsidiary of Grupo Aval Acciones y Valores, S.A.

The total amount in cash received by BBVA in connection with the sale of the mentioned interest amounts to, approximately, 645 million U.S. dollars (“USD”), of which, approximately 505 million USD have been received as purchase price and approximately 140 million USD have been received as dividends distributed by BBVA Panamá since June 1, 2013.

Madrid, December 19, 2013

SIGNATURE

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.