The two teams drew 1-1 on Tuesday in Lima.
Venezuela player Nahuel Ferraresi told local media that fingers on his left hand were injured by a baton-wielding Peruvian police officer who hit him twice as he tried to approach Venezuelan fans in the stands after the match. The outlets also showed video of the incident.
"Our federation will not tolerate, in or outside of Venezuela's borders, any degrading treatment toward our players, coaching staff or fans," the FVF said in a statement, adding it "energetically condemned aggressions, both verbal and physical."
The federation also criticised migration compliance checks it said Venezuelan fans were subjected to in order to enter the stadium.
The FVF also said on social media that its team's airplane was awaiting authorisation to refuel to leave Lima. The Peruvian foreign ministry denied any restriction on refuelling the aircraft and a ministry source told Reuters the plane left in the afternoon.
