Jones, who racked up 3.5 sacks in the past two games, suffered a biceps injury in Sunday's 24-13 win over the Texans.
Former University of Tennessee tight end Luke Stocker has been signed to take his place on the team's 53-man roster. Stocker worked out for the team last week.
Jones, a fourth-round draft pick in 2014 out of Penn State, has started all 12 games for the Titans this season. He had two sacks against the Colts on November 26 before adding 1.5 sacks on Sunday against the Texans, before his injury.
Stocker (6-5, 253) was a fourth-round pick of the Buccaneers in 2011, and he's played in 80 games during his NFL career. He was released last week by the Buccaneers.
During his playing career, Stocker has hauled in 52 passes for 400 yards and three touchdowns. He has earned praise for his blocking ability during his career.
The Titans face the Cardinals on Sunday in Arizona.
The Tennessee Titans take on the Houston Texans in Week 13 at Nissan Stadium. (Photos: Donn Jones, AP)