Ireland U-20 head coach Mike Ruddock said: "Unfortunately Tom broke his hand during the game against Fiji and will have to leave the tournament.
"Tom has been a major player all season and we are all very disappointed to see him leave like this. I would like to thank Tom for all he has given over the season and commend him on his achievements so far.
"This squad has shown remarkable resolve throughout the season. We have lost a number of prolific players, including Robbie Henshaw and Stuart Olding who were called up to the senior squad, but they have adapted and I am confident that they will adjust and are focused on the game against New Zealand."
Ruddock's charges are preparing to face the Baby Blacks in their final Pool B fixture at the Stade de la Rabine on Thursday (kick-off 6.45pm local time/5.45pm Irish time).
Carlow man Daly will be replaced in the Irish squad by Northampton Saints and Exile player Alex Wootton.