The stuntman Tom Sizemore ran over should make a full recovery ... we've learned his injuries were not as massive as first thought.

A rep for the actor tells TMZ the "Shooter" stuntman suffered 2 broken ribs and a wrist ... requiring surgery. A production source backs up the medical assessment.

TMZ broke the story ... Sizemore was behind the wheel when he hit the gas on a Cadillac SUV, running over and pinning the stuntman. He was airlifted to a local hospital.

Production sources say Tom was only supposed to jump in the vehicle ... not drive it. Tom says that's not true ... the scene called for him to drive away.

Tom says producers are not blaming him, and he also says, despite his history of substance abuse, he's clean.