Squire suffered the injury just before halftime in the pulsating Super Rugby clash in Dunedin.
He also broke his thumb during Super Rugby last year and was out for a similar amount of time.
The 26-year-old's return is timetabled for the Highlanders' matches in South Africa against the Bulls on April 28 and the Sharks on May 5.
Squire became All Blacks coach Steve Hansen's first-choice blindside flanker last year, effectively ending stalwart Jerome Kaino's international career.
Elliot Dixon replaced Squire on Saturday against the defending champions and provided a second-half spark for his side, who were far more controlled and precise after a frenetic first half.
The Highlanders, who are unbeaten and lead the highly competitive New Zealand conference, face the Hurricanes next week in Wellington.
(Reporting by Greg Stutchbury; Editing by Ed Osmond)
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