Clowney has been bothered by the ailment for the majority of the season. He failed to practice all week and has been listed on the weekly injury report since Week 5.
The injury sidelined him for Week 9, and he was reportedly considering undergoing surgery earlier this season to fix the issue.
A coveted free agent in the offseason, Clowney hasn't met expectations since signing with the Titans on a one-year deal. The 27-year-old pass-rusher has yet to record a sack and has just six quarterback hits.
The Titans had been counting on Clowney and Vic Beasley, signed from the Atlanta Falcons in the offseason, to improve their pass rush, but Beasley's time in Tennessee was cut short when he was released due to lack of production.
Clowney, a former No. 1 pick, has recorded just three sacks over the last two seasons.