The 25-year-old will miss Ireland’s games against Scotland and France after he was handed the ban at a disciplinary meeting in London.
Healy trod on Cole’s ankle after an Ireland maul had collapsed in an incident which was missed by referee Jerome Garces, sparking a large brawl.
As a result, Healy was cited for the alleged offence, with his ban being confirmed yesterday.
An independent disciplinary committee decided Healy’s actions should be categorised as a mid-range offence in terms of seriousness, which carries a sanction of five weeks.
The committee also allowed the maximum two weeks of mitigation, but by handing down a suspension of three weeks, recognised the player would not have played for his province this weekend and the ban will end at midnight on Sunday, March 10.
Replays clearly showed the Ireland and Leinster forward, a leading contender for selection to British and Irish Lions of Australia this summer, stamping on Cole.