"Vela says he is not 100 percent mentally and emotionally ready," the statement said.
Mexico coach Miguel Herrera, national team director Hector Gonzalez Inarritu and other FA officials met with the player in Madrid on Monday to discuss his availability but he was adamant he would not change his mind.
Vela, who has played for Arsenal and West Brom in England as well as Salamanca and Osasuna in Spain, has scored nine times in 35 internationals.
He played in the 2010 World Cup in South Africa, but fell out with the Mexico FA later that year after he was suspended for six months and fined after being accused of holding a party in a team hotel.
He returned to the national team in 2011 but refused selection for the London Olympics in 2012 when Mexico beat Brazil to take the gold medal.
Mexico are in Group A at the June 12-July 13 finals and will face Cameroon, hosts Brazil and Croatia.
(Reporting by Mike Collett; Editing by John O'Brien)
