After the game, Texans head coach David Culley told reporters Taylor "kind of pulled up" and that the injury was severe enough the quarterback couldn't continue. Culley wasn't sure if Taylor would be available Thursday night against the Carolina panthers.
Ian Rapoport of NFL Network later reported Taylor won't play in Week 3.
The veteran played the entire first half of the Week 2 game and excelled while going 10-of-11 for 125 yards and a passing touchdown to go with a 15-yard rushing score.
Taylor did not return in the second half as rookie Davis Mills replaced him in the Texans lineup. Mills, the team's third-round pick this year out of Stanford, finished 8-of-18 for 102 yards with a two-yard TD to Brandin Cooks and an interception.
Taylor signed with the Texans in March to mark his fifth team since the Baltimore Ravens selected him in the sixth round of the 2011 draft. He's also played for the Buffalo Bills, Cleveland Browns and Los Angeles Chargers, making 47 starts across his first 10 NFL seasons.
The 32-year-old Virginia Tech product opened the 2020 season as the Chargers starter, but he suffered a punctured lung during a pain-killing injection ahead of the team's Week 2 game. Justin Herbert took over the top spot on the depth chart and never relinquished it, even when Taylor returned to full strength.
Although Taylor has never quite established himself as a franchise signal-caller, he's been a reliable option when called upon, highlighted by ranking eighth in ESPN's Total QBR with the Bills in 2015.
The Texans will probably lean even more heavily on a rushing attack featuring David Johnson, Phillip Lindsay and Mark Ingram II with Taylor sidelined.