The Highlanders loose forward has had a set back in the recovery from a fractured thumb, picked up when the side played the Crusaders in March.
He is now expected to be back some time in June.
That does not bode well for Squire's chances of appearing in the All Blacks' series against France, which starts on June 9 and concludes on June 22.
The Highlanders have six games remaining before that series, however, he come into it with very little game time should he be fit and chosen.
"He had his cast taken off and under another scan it hadn't quite set how it was supposed to," assistant coach Mark Hammett said.
"So unfortunately it had to be reset and that reset the start date as well."
Squire has played 15 tests since making his debut in 2016.
Fortunately for the Highlanders, the blow comes in a position where there is plenty of depth to cover.
Shannon Frizell starred on the blindside flank in last week's win over the Blues, while Elliot Dixon has been bringing All Black experience off the bench.
Meanwhile prop Siate Tokolahi will miss four to six weeks with a medial cruciate ligament injury sustained last week against the Blues.