Cyprien suffered the injury on a non-contact play during Wednesday's practice.
"I am devastated to say that he tore his ACL," Vrabel said, per ESPN. "It's tough for me as a new head coach watching guys work hard in the offseason, play hard and not get a chance to experience the NFL season this year."
Cyprien recorded 57 tackles and one sack in 10 games last season with the Titans. He missed the start of the season with a hamstring injury after signing a four-year, $25 million contract.
The 28-year-old Cyprien has collected 511 tackles, three sacks and two interceptions in 70 career contests since being selected by the Jacksonville Jaguars in the second round of the 2013 NFL Draft.
In-house candidates Kendrick Lewis and Bryden Trawick are expected to compete for the starting spot opposite Kevin Byard.
In addition, free-agent safeties Kenny Vaccaro and Mike Mitchell are expected to work out for the Titans on Friday, NFL Network Insider Ian Rapoport reported.
Vaccaro recorded 60 tackles, three interceptions and 1.5 sacks in 12 games last season with the New Orleans Saints before landing on injured reserve. The 27-year-old told The Times-Picayune in March that he was fully healthy following core muscle surgery.
Mitchell spent the past four seasons with the Pittsburgh Steelers before he was released in March in a cost-savings move.
Vrabel said Thursday that the team will also reach out to former San Francisco 49ers safety Eric Reid's agent.
Reid claimed at the beginning of the offseason that he wasn't receiving interest from teams due to his decision to kneel during the national anthem. He was the first player to kneel alongside former 49ers quarterback Colin Kaepernick.
A Pro Bowl selection in 2013, Reid started 12 of the 13 games he played in with the 49ers in 2017, when he had two interceptions, four passes defensed, one fumble recovery and 66 tackles. He has 10 interceptions, 34 passes defended, one sack and 318 tackles in his career.