Freeney is suffering from an abdominal injury and did not accompany the team on the trip to Houston.
"He was getting better and moving along, but we just feel the best solution is for him to take a few more days to get ready," head coach Jim Caldwell told ESPN on Saturday.
Freeney and counterpart Robert Mathis are the leading pass-rushers on a Colts defense that has allowed the fewest points in the league this season. The Colts have held three opponents without touchdowns while compiling a 10-0 record that makes them one of the league's final two unbeaten teams.
Freeney did not practice all week and was listed as questionable, though following the team's final practice on Friday, Freeney said he definitely intended to play and would make whatever adjustments were necessary in terms of altering his pass-rush moves.
"We still have a good compliment of guys to rotate," Caldwell said.
Freeney played with the injury in last week's victory over the Baltimore Ravens, a game in which he finished with an empty stat line -- no tackles, sacks, quarterback hits or forced fumbles.
The Colts have dominated the series against the Texans but the games have typically been close, with the Colts winning by a field goal earlier this month. Freeney has contributed significantly. In 14 meetings with the Texans, Freeney has 12.5 sacks and three forced fumbles. In the Colts' victory earlier in the season, Freeney had one of his best performances of the year. He had 1.5 sacks and a season-high seven tackles against the Texans three weeks ago.
"He's as fine a player as I, an offensive coordinator, have tried to scheme against in all my years in football," Texans coach Gary Kubiak said this week.
Indy (10-0) can clinch the AFC South title with a win and a Jacksonville loss.
Information from ESPN's Ed Werder and The Associated Press was used in this report.