Clarke, a sophomore who was averaging 11.4 points and a team-leading 7.3 rebounds, suffered the injury in the second half of the Hokies' double-overtime win over Virginia on Sunday.
"Our hearts hurt for Chris," Virginia Tech coach Buzz Williams said in a statement. "He has worked really hard to become an outstanding player and an incredibly important teammate to what we are trying to build. I am confident that he will turn this situation into good and return next year an even better player, better student and better person."
Virginia Tech is 17-7 overall and 6-6 in ACC play. The Hokies have six regular-season contests left, beginning Tuesday night at Pittsburgh.