"The injury is not as bad as was first feared and it is expected that this will prevent him from playing for a period of three to four weeks."
A lay-off of such length will see O'Driscoll miss Ireland's final Six Nations tie next weekend against England, as well as Leinster's Magners League games against Glasgow Warriors (March 21) and the Llanelli Scarlets (March 29).
However, he could return in time for their league derby clash with Munster at the RDS on April 12.
Commenting on the injury on Sunday, Ireland coach Eddie O'Sullivan said: "Brian picked up the injury in a ruck. It's happened to him before. He was in the approach position, his foot slipped and he was hit from behind.
"This is the third time he's sustained the exact same injury. He got it in Rome three years ago and also for Leinster during a Heineken Cup game."