Milne felt discomfort in his left heel following the quarter-final against the West Indies on Sunday and subsequently underwent an MRI scan on Sunday afternoon.
The results showed significant swelling around the region rendering him unfit to play any further part in the tournament.
Henry, the 23-year-old Christchurch born fast bowler, has played eight One-Day Internationals and two T20 internationals for New Zealand to date.
Any injury or illness-based replacement requires a written submission to the Event Technical Committee along with a diagnosis from a medical practitioner as to the extent of the injury or illness.

Once replaced, a player may not return to the squad save as an approved subsequent replacement for another injured or ill player.
New Zealand will take on South Africa in the first semi-final of the ICC Cricket World Cup 2015 at Eden Park on Tuesday.

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