Colts owner Jim Irsay, announcing Luck's surgery in a tweet Thursday morning, said the outpatient procedure would not affect Luck's readiness for the 2017 season.
During the Colts' trip to London this season, Irsay said Luck did not have major problems with his right shoulder, which was initially injured in 2015, and would not need surgery.
Luck was listed on the team's injury report every week this season and was usually limited in practice on Thursdays, but he missed only one game in 2016: Week 12 against the Pittsburgh Steelers, after suffering a concussion.
After missing two games in 2015 due to the shoulder injury, Luck aggravated the injury while trying to make a tackle after throwing an interception against the Denver Broncos in Week 2 this season.
Luck threw for 4,240 yards with 31 touchdowns and 13 interceptions in 2016 as the Colts went 8-8 and missed the playoffs for the second straight season.
Information from ESPN's Mike Wells contributed to this report.