Savage was told on Friday that he would not need surgery, although the severe sprain could keep him sidelined well into the regular season.
After Cowboys defensive tackle Davon Coleman knocked the quarterback to the ground, Savage left the game with seven minutes and 15 seconds left to play. Ryan Mallett was sent into the game to replace him.
Savage, 25, was drafted by the Texans in the fourth round of the 2014 NFL draft. Last season, Savage played in two games with the Texans and completed 10 passes.
The Texans' regular season begins on Sept. 13 against the Kansas City Chiefs.
- Xandria James