The Harlequins flanker sustained the problem in his club's European Rugby Champions Cup victory over Leinster on Sunday.
Robshaw had already been ruled out of this weekend's return fixture, but is now not expected to play again until January - a matter of weeks before England's Six Nations campaign is due to get under way.
Announcing two changes to their starting XV for Saturday's clash at the Aviva Stadium, a Harlequins statement read: "Following consultation with a specialist, the RFU and the Harlequins medical team, Robshaw is expected to return in three to four weeks."
Robshaw and Nick Evans - also out through injury - are replaced by Jack Clifford and Tim Swiel for the Pool Two clash.
Harlequins currently sit three points clear of Leinster at the top of the group.