The 29-year-old All Black fell heavily in the match and sustained damaged tendons and as a result he has already undergone surgery in the 30-3 defeat in Cardiff.
Jack has been instrumental in helping Saracens to their first Heineken Cup quarter-final appearance and Saracens Director of Rugby Alan Gaffney admitted the giant second row would be missed by his side.
“It’s a blow for the club,” he said. “Chris has made a great impact since he arrived at the club and I know that he will still play an active role in supporting the guys.”
Gaffney added that the very presence of the Kiwi would strengthen the resolve of his side: “Even though he won’t be able to get out on the pitch, with his knowledge and experience he still has a very important role to play for us.”
Jack played in three of Saracens’ Pool 5 matches, and scored two tries in the round 5 demolition of former finalists Biarritz Olympique in a Heineken man of the match performance.