The club captain sustained the problem during the first half of Saturday's 1-0 victory over Celtic, with the centre-back being substituted before the break.
Hearts have now confirmed that the 33-year-old suffered a significant injury and will be sidelined for the remainder of 2018.
Manager Craig Levein told the club's official website: "It's obviously a very big blow. I'm gutted for Christophe. He's really never been injured before and has played a number of years at the highest level, so it's really bad luck.
"The reassuring thing is that this year we have squad depth and Aaron Hughes showed his quality when called upon against Celtic, so we have options going forward."
Hearts' win at the weekend has taken the club to the top of the Scottish Premiership standings.