The team did not disclose the nature of the injury to Smith, who appeared in 15 games and had one interception with the Titans in 2017, making one start.
A fifth-round pick of the Seattle Seahawks in the 2015 NFL Draft, Smith also started both playoff games for Tennessee last season.
The Titans also added a pair of defensive linemen to the roster, signing Johnny Maxey and Du'Vonta Lampkin. The team waived defensive lineman Claude Pelon with an injury designation.
The 6-foot-5, 283-pound Maxey spent the final month of the 2017 season on the Titans' practice squad. Maxey appeared in two games with the Pittsburgh Steelers in 2016.
Lampkin (6-4, 335) is an undrafted free agent out of Oklahoma. He appeared in 15 games over two seasons with the Sooners, recording 27 tackles, including 6.5 for loss, and 1.0 sack.
Pelon appeared in one game with the New York Jets in 2017, making a pair of tackles.