The 1999 World Cup winner arrived at Welford Road to provide some experience in the absence of so many players at the World Cup but he will now retire as a player.
Tigers forwards coach Richard Cockerill said: "Owen had a positive influence in the pre-season period here and captained the side on occasions in the pre-season fixtures.
"He suffered a groin injury in the opening weeks of the season which meant he did not make as many playing appearances as he would have liked, but having his experience around the place was certainly beneficial."
After playing throughout the pre-season programme, Finegan made his Tigers debut on the opening day of the season at Bristol.
"Owen was called out of the team run on the Saturday morning to attend the birth of his child but then drove down to Bristol to join the team on the Sunday and played his part in a good win for us at a place where we have struggled in previous seasons. That is just the kind of spirit we have in the squad," added Cockerill.
"He has had a magnificent playing career with club and country, and we wish him well for the future."