Gareca praised the response from his Russian hosts after Farfan was rushed to hospital on Saturday after being knocked out in a clash of heads during training.
"He was unconscious for a couple of minutes," Gareca said. "He was assisted and stabilised and he is now in hospital. There are protocols in terms of recovery, so those make it mandatory for him to remain in hospital for 72 hours.
"That was what Russia established. He could be released from hospital but we understand the care of players is a priority for Russia and so thanks to the organisers and all the medical help that was provided."
The update comes just five days after Morocco included Nordin Amrabat in their second Group B match against Portugal after he was hospitalized for a concussion in their opener against Iran.
The North Africans were criticised for their reaction, especially after Amrabat removed his head protection 16 minutes into the game.
World players' union FIFPro called it "yet another alarming example of a player being put in harm's way".
