Team owner Jim Irsay announced the news via Twitter on Thursday morning. Irsay said Luck would be ready for the start of the 2017 regular season. It is not known whether Luck's offseason availability will be impacted by the operation.
Luck said at the season-ending press conference at the Colts' facility that he didn't think surgery would be necessary. Irsay told NFL Network last month that the Colts were not considering surgery as an option.
But with the Colts out of the playoffs for a second consecutive season, Luck opted to have the injury repaired.
No quarterback has taken more hits than Luck since he was the first overall pick in the 2012 NFL Draft.
Luck missed one game in 2016 with a concussion but was listed on the injury report every week. He missed two games in 2015 with a shoulder injury.