Mallett suffered the injury in his first career start Nov. 6 against the Cleveland Browns. He practiced fully all week but was on the injury report with a chest injury throughout the week leading up to the game.
The Houston Chronicle and Houston's FOX 26 earlier reported the injury.
Mallett will have an MRI to determine the extent of the injury. He could miss several weeks, which would further delay the beginning of an NFL career that has already taken a while to get started.
The Texans turned to Mallett just before their bye week. Mallett replaced former starter Ryan Fitzpatrick, a 10-year veteran. The Texans traded for Mallett on Aug. 31; he had spent the first three years of his career with the New England Patriots. Mallett threw only four passes in that time and never played a meaningful snap.
The Texans acquired him for a conditional draft pick. The pick is a sixth-rounder if Mallett plays 40 percent of the team's snaps this season and a seventh-rounder if he does not meet that condition.
In his first start Nov. 16, Mallett completed 20 of 30 passes and threw two touchdowns and one interception. He had the 10th-best QBR of any starting quarterback since 2001. On Sunday against the Bengals, Mallett completed only 21 of 45 passes and was likely hindered by the injury.