The injury, which he suffered on Tuesday, will require surgery.
Robinson played in all 13 games last season, starting three. He tallied 42 tackles, including three for loss, to go along with four pass breakups and two fumble recoveries.
The loss of Robinson puts a dent into an already inexperienced secondary, which looks to replace all four starters, including Tampa Bay Buccaneers third-round pick Mike Edwards.
"You know, it was unique to have that amount of experience in our secondary with one group," coach Mark Stoops said at SEC media days last week. "And that is hard to replace. As I mentioned, I feel like we have some inside guys -- some nickels, dimes, safeties -- that have played, that got their feet wet. Outside of corner, that's going to be the biggest issue with the experience out there.
"You do have Cedrick Dort coming back where he played two years ago. ... Brandin Echols comes in from junior college, so he has some experience as well. Jamari Brown is guy that redshirted a year ago that has the physical tools to be successful."
Kentucky, which had its best season under Stoops last year, winning 10 games for the first time in 41 years, opens the 2019 season against Toledo at home on Aug. 31.