The players - Nestor Vidrio, Israel Jimenez, Jonathan Dos Santos, Jorge Hernandez, David Cabrera, Marco Fabian, Javier Cortes and Nestor Calderon - were also fined 50,000 Mexican pesos (around £2,640) each.
The Mexican federation have not disclosed details of the incidents, which reportedly took place after Saturday's 1-0 Copa America warm-up win over Ecuador, but revealed the players involved were sorry for their actions.
Mexico team director Hector Gonzalez Inarritu said: "We do not go into details. They violated the rules, violated a code of discipline, and we had to act.
"The suspension is very painful for us, one week before starting the Copa America.
"The players confessed and are repentant. They have offered an apology to the fans, the team, coaching staff, the federation. I speak not of the facts (of what happened) but of the consequences."