[3] Born in Mexico City, Meza made his senior debut with Toluca on 2 September 2000, in a 3–2 home win over Celaya.

[1] Shortly after retiring, Meza became his father's assistant coach at Pachuca, being a part of the staff when the club won two CONCACAF Champions' Cups and the 2007 Clausura.

In 2009, while scouting for players in Ghana, due to heath scares about influenza, he was arrested for three days before being deported back to Mexico through Nigeria, despite having a permit to transit in the country.

[14] In 2012, with the authorization of General Secretary: Horace Reid, Enrique consulted on technical analysis and report for the Jamaica Football Federation during the 2014 FIFA World Cup qualification matches for CONCACAF region.

[15] On 16 May 2014, Costa Rican side Santos de Guápiles announced Meza as the club's technical director and head coach.

[28] In June 2019, Meza returned to his home country to join his father's staff at Veracruz, as an assistant coach.

[33] On 7 November 2021, Peruvian side Carlos A. Mannucci announced that Meza will serve as their head coach for the 2022 season.