The New Zealand fast bowler had an MRI scan after arriving in Hamilton yesterday to ascertain the damage he suffered during Sunday night's opening one-day international.
More information is expected this morning but even a conservative estimate for minor damage suggests Milne will be out until at least the end of the ODI series on January 31.
It is notoriously hard to pinpoint a return time for side strains but medical advice suggests most take four to six weeks to heal to a point where a fast bowler could resume at full pace.
The dejection on Milne's face was palpable during the match, as the injury threatened to end a seminal summer.
Midway through his eighth over he spoke to captain Brendon McCullum about the niggle.
It was the start of his third spell in a match which had him regularly clocking in excess of 150km/h - the speedball radar counted eight occasions.
It's understood Milne wanted to continue but McCullum advised otherwise. The 21-year-old left the field.
McCullum said: "It's tough for Milny to get injured bowling at that pace ... It doesn't look great."
Fellow bowler 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."
Milne has been cast as "the new Bond" but needs a chance to settle if he's to sustain a career rather than being remembered for a fleeting link with the number 150.
The World T20 scheduled for Bangladesh (or possibly Sri Lanka or India) in March might be a logical return date.
- Andrew Alderson of the Herald on Sunday