Allen suffered a back injury and Milne picked up an ankle problem during training ahead of the team's departure for the five-match T20I series.

Allen, the powerful opening batter who has a T20I strike-rate of 163.60, would be certain of his place in New Zealand's T20 World Cup squad. Milne, who has had an injury-hit career, is less assured of a spot in the final 15 for the USA and Caribbean depending on how many quick bowlers are taken.

"We feel for both Finn and Adam, suffering injuries so close to the start of the tour. They have been strong performers for us in the T20 format since the last World Cup," New Zealand coach Gary Stead said.

"Our support staff and medical networks will be working closely with both players over the next few weeks to complete plans for their treatment and subsequent return to cricket."

"Zak has had an impressive season for Canterbury including being their leading wicket taker in all three competitions," Stead said. "He has displayed impressive skills with the ball, particularly in T20 cricket for the Kings. We also know he has skills with the bat and it will be an excellent opportunity for him to be part of the group."

New Zealand were already without nine players for the Pakistan tour due to IPL commitments while Will Young (county cricket), Tom Latham (paternity) and Tim Southee (strength and conditioning) were also not available.

The initial T20 World Cup squad needs to be named by May 1 but can be freely amended until May 25.