No additional details were given concerning Davis' absence.
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 ESPN's Adam 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.