The centre had to leave the field of play during the 56-27 Champions Cup quarter-final victory but Saracens say they are still waiting to learn the full extent of the damage.
Barritt has undergone scans on the problem, and the club have indicated it does not look serious.
However much will depend on how he responds to treatment this week.
A statement on the club's website read: "Scans were relatively positive and the timeline for Barritt's return will be determined by how he responds to treatment over the coming week."
This weekend's Premiership clash with Newcastle Falcons at Allianz Park is sure to come too soon for Barritt, who will face a race against time to make the semi-final encounter with Munster on April 20.