He was later transported to the University of Mississippi Medical Center where his leg was amputated. He remains in a critical condition.
The New York Post reported Branch was expected to survive, but had a number of complex surgeries ahead of him.
Branch's friend, Micah Heckford, was with Branch on the trip and told the Mississippi Clarion Ledger the incident raised reasons to rethink gun safety.
"All of us have hunted for 20 years or more and none of us thought about that happening," Heckford said. "We were just moving 200 yards to set up and hunt. The opportunities for an accident are there and we just don't realise it. We think we're being safe, but are we? If there's a shell in that gun, anything can happen."