Heaslip appeared to be kneed in the back by Pascale Pape during Ireland's 18-11 win over France on Saturday. The France lock has been cited following the incident.
"Scans have revealed fractures of the transverse process of three vertebrae in Jamie's back," the Irish RFU said in a statement on its website.
The injury is not expected to cause any long-term problems."Jamie is already feeling more comfortable and it is hoped that he will be available to play again in approximately four weeks," the ruling body said.
Heaslip will miss Ireland's next game against England in Dublin on March 1, a potential title decider, and probably the trip to Wales on March 14.
(Reporting by Ed Osmond in London, editing by Justin Palmer)
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