Johnson told The Tennessean he suffered the injury in Week 3.
"It's nothing major," he said in a text message to the paper. "People don't know I been playing with it since week 3 of the season."
Johnson rushed for 90 yards in Tennessee's 20-17 Week 3 victory over the San Diego Chargers.
The three-time Pro Bowler is expected to need at least a month to recover from the operation, according to multiple media reports.
Despite the injury, Johnson rushed for 1,077 yards and six touchdowns this season.
The 28-year-old Johnson told The Tennessean earlier this month that he believes he has been underused in the Titans' offense and acknowledged he would be open to a trade.