Milne left the field during the fourth match in Nelson after a tidy display in which he took two for 28 from seven overs. There is not understood any form of tear.
Coach Mike Hesson confirmed the news after today's media conference.
"Adam won't play this game but he's scrubbed up pretty well. It's nothing major but we're being cautious.
"He will start bowling hopefully before the next game. Unless he's fully pain free and without incident, he'll probably be ready for the last game of the series.
"He bowls [at around] 150km/h so when he does get a bit of a twinge it's not worth pushing through."
Hesson said Milne would not be rested until the World Cup opener on February 14.
"He still needs [to work on his] skills so you can't put someone away and hope their skills will be up to speed later.
"We've got five quicks to share around and Adam's played enough of these games [three] already so he's good from a skill perspective. Some time on the sidelines is not such a bad thing."
Milne has become an increased menace for opposition of late as his erratic pace has morphed into sustained accuracy.
Since the Pakistan ODI series in December, Milne has taken nine wickets in seven matches at 32.22 compared to a career average of 45.63; he's taken a wicket in all but one game and dismissed Kumar Sangakkara in each of his three innings this series.
Milne's economy rate has also dropped to 4.71 in ODIs this season compared to 5.10 overall. As an indicator of his increased control, he's exceeded five runs an over twice.
He shapes as a World Cup weapon for New Zealand. While he's not considered a top tier player, his venom holds an element of surprise. Teams will analyse video footage but only Pakistan and Sri Lanka have faced him for a sustained period at international level.
Kyle Mills had a sustained bowl at training. Hesson confirmed he would play one of the two matches in Dunedin.
By Andrew Alderson of the Herald on Sunday in Dunedin
