The 30-year-old, who made the last of his 16 appearances for Wales in 2012, has been unable to recover from a third operation to cure the problem.
Bishop joined Ospreys in 2005, making 209 appearances for the region.
"If there is ever a player who illustrates everything that an Osprey should be, it's Andrew," said coach and former team-mate Steve Tandy.
"It's been a privilege to work with him, both as a coach and playing alongside him from when he first came into the squad as a youngster."
Tandy described Bishop as a "tough cookie".