Houston, who left last week's game against Jacksonville with a sore hamstring and did not return, was not scheduled to practice on Wednesday.
Chiefs coach Andy Reid said it was "a stretch'' that Houston would be available against the Patriots. Houston is third on the Chiefs with three sacks.
The Chiefs are preparing rookie Breeland Speaks, a second-round draft pick, to replace Houston. In limited playing time this season, Speaks has five tackles and no sacks, but he did recover a Jacksonville fumble last week.
The Chiefs defense has struggled this season, giving up an NFL-worst 462 yards per game. But their high-powered offense is averaging 35 points per game, second best in the league, and 413 yards per game, fourth best in the league, on the way to a 5-0 record.
The Chiefs also learned that guard Laurent Duvernay-Tardif, who broke his leg against the Jaguars, has torn ankle ligaments. The Chiefs placed Duvernay-Tardif on the injured reserve list, but Reid remained hopeful that he could still play again this season.
"It was a little bit worse than what we originally thought, but not to the point where potentially he can't come back this year,'' Reid said.