Davis did not travel with the team and no additional details were given by the Colts, but a source told ESPN's Adam Schefter that Davis stayed behind to receive treatment for a lingering groin issue.
Cornerback Rashaan Melvin is expected to return against the Texans after missing last week's game. Rookie cornerback Quincy Wilson already was ruled out with a knee injury.
The Colts tried to trade the 29-year-old Davis, whose contract is up after the season, at the trade deadline but found no takers, sources told Schefter.
Davis has been with the Colts since 2012 and was a Pro Bowl selection in 2014 and 2015. However, Davis started this season and last season with injuries. He missed the first two games of 2016 because of a foot injury, and missed the first four games of this season rehabbing a groin injury.
Davis has 22 career interceptions and 344 career tackles entering Sunday's game.
The Colts (2-6) are currently in last place in the AFC South.
The Associated Press contributed to this report.