Henshaw appeared to dislocate his shoulder as he scored his second try of the comfortable win in Dublin, the Leinster back leaving the field with his injured right arm in a sling.
Coach Joe Schmidt had hoped there would be good news about the centre, but scans on Monday confirmed Henshaw would need an operation.
The 24-year-old has already had surgery to correct the problem but that means he will play no further part in the tournament.