The 27-year-old, who joined the Premiership outfit on a season-long deal from the ACT Brumbies in October, sustained the injury while playing for the Chiefs against Saracens last weekend.
"In a tackle against Saracens, Len has picked up the injury and it's going to require surgery," Exeter said in a statement.
"The good news is that we can get him in for the operation pretty quickly, though unfortunately it does mean he will miss the block of games over the festive period and into the cup competitions in the new year.
"We're looking at him being back fully fit and ready to play the remainder of the season post the Prem Rugby Cup block which overlaps with the Guinness Six Nations."
Ikitau, who has 47 caps for the Wallabies, has played five times for the Chiefs in all competitions, scoring two tries.