The news extends an annoying run for Milne, who is also set to miss the World Cup, due to not being able to prove himself in any format over the past few months.
While he could have made a late charge or put his hand up as a first-choice injury replacement with a strong IPL, he is now set to potentially have to wait until county cricket season before he can get back to the bowling crease.
Black Caps captain Kane Williamson was also unlikely to be thrust into IPL action, with his shoulder injury still a slight concern.
Williamson's Sunrisers Hyderabad side started their season against the Kolkata Knight Riders overnight, but coach Tom Moody indicated they would remain cautious with the star batsman, who had suffered the injury during New Zealand's second test against Bangladesh in Wellington earlier this month.
"We have got quite a few days before our next home game. If he's not available, I don't see any issues. Bhuvi [Bhuvneshwar Kumar] will lead our side since he's our vice-captain," said Moody.
Williamson is still set to play a major part in the IPL, having arrived in India on Friday night alongside Martin Guptill, and has been retained as Sunrisers skipper despite the return of former captain David Warner after his ban for ball tampering.
"Kane is an outstanding batsman and also a highly respected international player. He has stepped in for us last year and has shown good leadership qualities," said Moody.