The 31-year-old has damaged three vertebrae after appearing to be kneed in the back, while playing for Ireland, by France second row Pascal Pape on Saturday.
Heaslip - who has made seven GUINNESS PRO12 appearances this season - will definitely miss Ireland's game against England on Sunday March 1.
Yet Ireland have eased fears it could be a long-term setback for the Leinster star.
"Scans have revealed fractures of the transverse process of three vertebrae in Jamie's back," read the statement from the IRFU.
"Although this injury causes a good deal of discomfort it does not impact on the structural integrity of the spine, and once healed should pose no long term issues. Typically this injury is treated akin to a soft tissue injury; according to symptoms.
"Jamie is already feeling more comfortable and it is hoped that he will be available to play again in approximately four weeks."
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