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.
There was better news regarding Tadhg Furlong, though, after he limped out of the Italy win.
Scans on the forward showed he had only suffered a "minor hamstring injury" and Ireland expect him to be fit to face Wales at the Aviva Stadium on 25 February.