The team also officially announced the addition of linebacker Erik Walden to take Tretola's roster spot.
Tretola, a Titans' 2016 sixth-round draft pick who played in one game last season, was released from the hospital Sunday with what the team called "a minor injury." He was waived with a non-football injury designation Friday.
Tretola and Titans receiver Tajae Sharpe were also accused of assaulting a man outside a Nashville bar in April. Neither player has been charged and the case is being investigated as a civil matter.
"First of all, [Tretola] couldn't practice with the injury that he had. Second, he made some poor decisions and it wasn't strictly the two offseason incidents that made that decision," Titans coach Mike Mularkey said.
The Titans also signed rookie offensive lineman Jake Simonich and released linebacker Johnny Ragin.
Rookies and veterans reported to training camp Friday. Practice begins Saturday.