Martino said Vela was excluded from the squad for this summer's tournament at the player's request. The Argentine explained that Vela, who has scored 12 goals in 12 matches this season for LAFC, preferred to remain with his club and spend time with family.
"I spoke with Carlos Vela over the phone last week and he assured me that at this time his club and his family are his priority, that's why he stepped aside," Martino said, according to Tom Marshall of ESPN FC.
Hernandez, Mexico's all-time leading scorer, also asked to be omitted from the team in order to attend the birth of his first child, which is expected to take place during the Gold Cup.
Meanwhile, Hirving Lozano was included despite uncertainty over his availability after he suffered a knee injury last month.
Here is Mexico's 29-man preliminary squad ahead of friendlies against Venezuela and Ecuador:
Goalkeepers: Guillermo Ochoa (Standard Liege), Jonathan Orozco (Santos Laguna), Raul Gudino (Chivas), Hugo Gonzalez (Necaxa)
Defenders: Hector Moreno (Real Sociedad), Diego Reyes (Leganes), Nestor Araujo (Celta de Vigo), Jorge Sanchez (America), Jesus Gallardo (Monterrey), Miguel Layun (Monterrey), Cesar Montes (Monterrey), Carlos Salcedo (Tigres), Luis Rodriguez (Tigres), Fernando Navarro (Leon)
Midfielders: Andres Guardado (Real Betis), Jonathan dos Santos (LA Galaxy), Erick Gutierrez (PSV Eindhoven), Carlos Rodriguez (Monterrey), Luis Montes (Leon), Edson Alvarez (America), Ivan Rodriguez (Leon), Orbelin Pineda (Cruz Azul)
Forwards: Hirving Lozano (PSV Eindhoven), Raul Jimenez (Wolves), Alexis Vega (Chivas), Roberto Alvarado (Cruz Azul), Rodolfo Pizarro (Monterrey), Uriel Antuna (LA Galaxy), Marco Fabian (Philadelphia Union)