That leaves Jacoby Brissett in place as the team's starter.
Brissett has been solid if unspectacular since taking over as the team's starter for Scott Tolzien, throwing for 997 yards, two touchdowns and three interceptions in five games. He's also completed just 60.6 percent of his passes and rushed for 83 yards and another three scores.
Without Luck, the Colts have started the season 2-3.
Luck has yet to play in a game this season after undergoing offseason shoulder surgery. While he was able to practice last week in a limited capacity, it remains unclear when he'll be able to make a full return.
Without Luck, the Colts find themselves devoid of their franchise player. In 15 games last season, he threw for 4,240 yards, 31 touchdowns and 13 interceptions, completing 63.5 percent of his passes.
Injuries have become a major storyline in his career, however. He missed nine games in the 2015 season due to a lacerated kidney, and he confirmed in April that his recent shoulder injuries dated back to that season.
"It originally occurred a couple years ago against [Tennessee in Week 3]," he said, per Marc Sessler of NFL.com. "We sort of sat down after that year and felt like rehab (last offseason) was the way to go, and I think that was (the) absolute correct decision, we did some awesome things. This year happened obviously and (it) transpired through this year, and (we) sat down after this year and decided that maybe it was time to do surgery on (the shoulder)."