The news follows his team's shock 2-0 loss to old rivals the United States in the second round of the World Cup finals.
Garcia Aspe, 35, told Radio Formato 21: "I've played my last game, it's time to stop."
The veteran midfielder came on as a substitute in the 78th minute of a match in which Mexico failed to continue their impressive form of the group stages.
Nicknamed 'Captain Courage', Garcia Aspe played in Mexico's last three World Cup campaigns.
At club level he has played for University of Mexico and River Plate in Argentina as well as Mexican sides America, Necxa and Puebla.