The Argentina international sustained the injury in the first half of Sunday's 1-0 Serie A derby triumph at Torino following a heavy challenge from Ciro Immobile.
Tevez needed stitches to patch up the wound on his right ankle and is now facing a race against time to face the Turkish side.
A statement from Juventus read: "Carlos Tevez sustained a lacerated and contused wound on his right ankle.
"The striker's condition will continue to be assessed over the coming hours, but he remains a serious doubt for Wednesday night's Champions League game against Galatasaray."
Tevez, who is Juve's top scorer this season alongside Arturo Vidal with three goals, was furious that Immobile was not sent off.
Tevez shared several photographs of his injury on his Twitter account and tweeted a comment that read: "It's only a yellow card for the person that almost broke my ankle."