Luck was not a participant at Tuesday's first OTA session. The Colts said he will be re-evaluated heading into next week.
"Just a little tweak; little strain," Colts coach Frank Reich told reporters. "So my whole mode -- and our whole mode -- is going to be during this session just to be real conservative with anybody who has any issue whatsoever."
"Where we're at right now is we'll just say, 'Hey, play conservative this week. Nothing this week, and then we'll re-evaluate it after this week and see where he is.'"
The Colts have OTAs through Thursday, before returning for a second session from May 29 to 31. The final OTA session is from June 3 to 6. Indianapolis had mandatory minicamp from June 11 to 13.
Luck, 29, was the 2018 AP Comeback Player of the Year after completing 67.3 percent of his throws for 4,593 yards, 39 touchdowns and 15 interceptions in 16 starts last season. The resurgence came after he missed the 2017 season with shoulder issues.
Luck made his fourth Pro Bowl last season. The No. 1 overall pick in the 2012 NFL Draft signed a five-year, $122.9 million contract with the Colts in 2016.