Milne, who returned with figures of one for 40 from his 7.3 overs in the first ODI, had an MRI scan after arriving here to ascertain the damage.
According to a report in the New Zealand Herald, Milne will be out of action until at least the end of the ODI series against India.
The report added that according to medical advice Milne will take at least four to six weeks to get back to his full shape.
Milne, who continuously clocked speed in excess of 150km/h in the first ODI, suffered the injury midway through his eighth over and the start of his third spell.
"It's tough for Milne to get injured bowling at that pace ... It doesn't look great," McCullum was quoted as saying by the newspaper.
Milne's pace colleague Mitchell McClenaghan said he was "absolutely gutted for the man".
"He had his (T20I) debut (as an 18-year-old in 2010), went back (to domestic cricket) worked on his accuracy and returned.
"To see someone bowl that quick and accurately is a throwback to the Shane Bond days," McClenaghan said.


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