Welker caught a pass from Tom Brady on New England's first possession and his knee appeared to buckle as he turned upfield. Trainers helped Welker off the field and he was taken to the locker room on a cart.
Welker entered the game with 122 catches for 1,336 yards and four touchdowns this season.
Brady started despite a rib injury. A Patriots spokesman said he was not aware of Brady having broken ribs, despite a CBS Sports report.
The Patriots' defense stopped Houston at the 1-yard line late in the first half, and rookie Brian Hoyer replaced Brady. Hoyer handed off to Fred Taylor on his first snap, Taylor fumbled and safety Bernard Pollard -- infamous in New England as the player who ended Brady's 2008 season just minutes into the opener -- recovered in the end zone to give the Texans a 13-10 lead.
Brady was 10 for 14 for 135 yards when he departed. He returned for the Patriots' first series of the second half.
New England center Dan Connolly left in the second quarter with an ankle injury, and the team said his return was questionable.