Milne was forced to leave the field midway through his eighth over and had scans in Hamilton on Monday.
New Zealand Cricket physiotherapist Paul Close said Milne would need at least six weeks rehabilitation, ruling him out of the remainder of India's tour.
The Central Districts bowler had struggled on flat wickets on tours in Sri Lanka, India and Bangladesh but caused a stir this summer on New Zealand wickets with his fastest deliveries being clocked in excess of 153kph.
Canterbury pace bowler Hamish Bennett will replace Milne in the squad for the remainder of the one day international series.
The second game in the five-match series is on Wednesday in Hamilton.
(Reporting by Greg Stutchbury; Editing by Peter Rutherford)
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