“We’re all gutted for Adam,” coach Rob Walter said. “He’d worked so hard to get himself ready for the tournament and was looking back to his best in his eight games for the Eastern Cape Sunrisers.
“It’s unfortunate timing for Adam and we wish him a speedy recovery.”
Milne’s exit is a blow to New Zealand’s fast bowling stocks as Matt Henry and Lockie Ferguson likely to miss parts of the World Cup on paternity leave.
Ferguson is also returning from a calf injury sustained in the UAE’s ILT20.
Kyle Jamieson has been added to the squad, after being named as a travelling reserve.
“It’s great that Kyle is already with us here in India,” Walter added.
“He’s an integral member of our pace-bowling group and has hit the ground running on this tour.
“He’s a hard worker with a good set of skills and experiences that will hold him in good stead for the tournament.”
Jamieson, 31, was also rushed into the Black Caps’ squad for last year’s Champions Trophy in Pakistan, after Ferguson was forced out at the last minute with injury.
There, he took three wickets in four games as New Zealand reached the final, where they were beaten by India in Dubai.