Events in the year 1956 in Mexico.

• President: Adolfo Ruiz Cortines
• Interior Secretary (SEGOB): Ángel Carvajal Bernal
• Secretary of Foreign Affairs (SRE): Luis Padilla Nervo
• Communications Secretary (SCT): Carlos Lazo
• Education Secretary (SEP): José Ángel Ceniceros
• Secretary of Defense (SEDENA): Matias Ramos
• Secretary of Navy: Roberto Gómez Maqueo
• Secretary of Labor and Social Welfare: Adolfo López Mateos

• President of the Supreme Court: Vicente Santos Guajardo

• The Chemical Society of Mexico is formed.
• April 30: The opening of the Torre Latinoamericana.

Belisario Domínguez Medal of Honor – Gerardo Murillo ("Dr. Atl")

• List of Mexican films of 1956

• 1955–56 Mexican Primera División season
• The Diablos Rojos del México win the Mexican League.
• Mexico participate at the 1956 Summer Olympics.
• Establishment of the Mexican Center League.
• January 1: Club de Futbol Ballenas Galeana Morelos is founded.

• March 23 — Fidel Demédicis Hidalgo was a federal senator from Morelos (2012-2018)
• April 21 — Ángel Aguirre Rivero, constitutional Governor of Guerrero 2011–2014 and interim Governor of Guerrero 1996–1999
• May 8 — Javier Álvarez, composer (d. 2023)
• June 8 — René Juárez Cisneros, Governor of Guerrero 1999-2005 and current federal Senator (d. 2021)
• June 15 — Francisco Olvera Ruiz, Governor of Hidalgo 2011–2016
• June 22 — Manuel Saval, soap opera actor (Simplemente María (1989 TV series)) (d. 2009)
• July 31 — Laura Zapata, Mexican telenovela actress, singer and dancer^{[citation needed]}
• August 15 – Arnulfo Mejía Rojas, engineer, architect, teacher, historian, painter, artist, and Catholic priest, best known for being the creator of "The Boat of the Faith" (d. April 18, 2016).
• September 8 – Ricardo Torres Origel, Mexican politician (PAN) Deputy (2000-2003) and Senator (2006-2012) from Guanajuato (d. April 24, 2016).
• October 13 — Ana Bertha Espín, actress
• October 19 — Francisco Rojas San Román, politician from the State of Mexico (d. 2018).
• Date unknown — Rosario Robles, politician, acting Mayor of Mexico City 1999-2000