Burkhead, 31, was playing on a one-year, $1.5 million deal after joining Houston in June.
In 15 games this season, Burkhead has run for 403 yards and three touchdowns on 110 carries. Burkhead took over as Houston's starting running back in Week 11 and has carried the ball 103 times in the last seven weeks.
"He's been Mr. Consistent for us," coach David Culley said last month. "He's a guy that's going to get north and south. He knows how to play."
Burkhead ran for a career-high 149 yards and two touchdowns on 22 carries in Week 16 against the Los Angeles Chargers.
The Texans started the season with five running backs on the roster, but during the season traded Mark Ingram II to the New Orleans Saints, waived Phillip Lindsay and lost Scottie Phillips to injury. Houston enters the final week of the regular season ranked last in Football Outsiders' DVOA.
Burkhead spent the previous four seasons with the New England Patriots, where Texans general manager Nick Caserio was director of player personnel.