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".
He added: "His consistency was his trademark, which is why he made such an impact and managed so many appearances, year in, year out, despite having to compete with some great players in his position.
"It's a sign of his quality that despite that competition for places, he was such an influential member of the squad over 11 years, playing a big part in our various successes on and off the field."
Bishop was capped at all age-grade levels by Wales before winning his first senior cap on the South Africa tour of 2008.