Cichy, a senior, will have knee surgery Friday.
"You hate it for Jack," Chryst said in a statement Thursday. "You only get so many chances to play this game and you never want to see a guy miss any of those opportunities. He's one of the leaders of our team and I know he'll be a big part of what we do moving forward this season."
Cichy has dealt with other injuries in his career, missing seven games last season after tearing a pectoral muscle. Despite missing most of the season, Cichy was still named All-Big Ten honorable mention after recording 60 tackles and seven tackles for loss.
The veteran linebacker was set to be a captain for the Badgers this season and figured to be a big part of new coordinator Jim Leonhard's defense.
Cichy was scheduled to start alongside junior T.J. Edwards, who had a team-high 89 tackles last year. Junior Ryan Connelly filled in last season after Cichy went down and finished with 59 tackles in 14 games.
The Associated Press contributed to this report.