The Colombia striker joined Rudi Garcia's side on an initial loan deal on Sunday, with Roma able to make the move permanent for €12.5 million at the end of the campaign.
Ibarbo made his Roma bow as a substitute in Tuesday's 2-0 Coppa Italia quarter-final defeat to Fiorentina, but he will now be forced to spend a spell on the sidelines.
A club statement read: "Ibarbo underwent medical tests today [Thursday] that confirmed a grade one/two injury to the myotendinous junction of his right medial gastrocnemius muscle.
"The player has already started treatment on the injury."
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