LAFC forward Vela's omission was due to the player preferring to be with his club and family, said Mexico coach Gerardo "Tata" Martino, and comes after the 30-year-old has recorded 12 goals and six assists in 12 MLS games in 2019.
"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," said Martino in the news conference in Mexico City.
West Ham United striker Hernandez asked permission to be absent due to birth of his first child, which is scheduled to take place during the tournament, and was expected, while Porto midfield Hector Herrera asked not to be called in after a long season and pending club move, reported to be to Atletico Madrid.
Porto winger Corona missed out after a back-and-forth in March about his fitness for friendlies against Chile and Paraguay. Martino was livid that Corona hadn't turned up to his first camp as El Tri coach and was open in expressing that.
Martino said that he hadn't spoken to Corona since then and that after weighing up his options decided against calling in the player, who has been in good form with Porto.
Former Barcelona coach Martino said in his time managing the Argentina and Paraguay national squads he hadn't experienced a similar situation of a number of players asking not to be called up.
"I don't think it is common. It's not something I've seen before," said Martino. "A call-up to the national team is a prize for footballers and when they don't see it as that, it's logical for them not to be here."
There was some positive news with PSV Eindhoven's Hirving Lozano on the list, although there is still some doubt whether he'll recover from the knee injury picked up on April 25.
Real Betis youngster Diego Lainez and Leon striker Juan Jose Macias are both in Mexico's Under-20s squad for the World Cup and weren't taken into consideration.
There were call-ups for youngsters Carlos Rodriguez (Monterrey), Roberto Alvarado (Cruz Azul) Jorge Sanchez (Club America), Raul Gudino (Chivas), Ivan Rodriguez (Leon) and Edson Alvarez (Club America).
The squad will be cut to 23 players in the first week of June ahead of the Gold Cup, which Mexico kicks off on June 15 against Martinique, followed by matches against Canada (June 19) and Cuba (June 23).
Mexico warms up for the Gold Cup with games against Venezuela (June 5) and Ecuador (June 9).
The 29-player squad in full:
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)