Trouba has been one of the team's top blue-liners this season with 12 points (four goals, eight assists) in 31 games.
"He's had a kind of pre-existing condition that most players deal with," head coach Paul Maurice said Tuesday. "And what you're hopeful for is that it heals, it gets better and progresses, and he had the opposite experience.
"Things started to get progressively a little bit worse on him and it just got to the point that the only and best way for us to get him back to 100 per cent is (we) have to shut him down."
Trouba, 20, had 29 points (10-19) in 65 games last season. He was drafted by the Jets with the ninth overall pick in the 2012 NHL Entry Draft.