Cabanas, 29, was shot after an incident in the city. The Club America striker was taken to a hospital intensive care unit.
Mexico City attorney general Miguel Angel Mancera told TV station Televisa: "We don't clearly know the motive behind the injury. According to an initial report it was a shot from a firearm with a frontal entry point and without exit.
"The player is conscious but he has a heart problem which they're trying to stabilise."