Squire, who turns 28 tomorrow, picked up the injury at training late last week and is now set for more time on the sidelines.
Highlanders coach Aaron Mauger said Squire had torn the medial ligament in his knee.
''It is a terrible blow for him. The guy has worked so hard to get back to where he is.
''These things happen in rugby and unfortunately they have happened to a guy who has already had a bit of adversity this year,'' he said.
''He has had some poor luck, all right.''
It is a big blow for Squire who has not played at all this season. He was suffering from a hip injury and did not play in the opening month but after some gradual improvement got back on the training field fully last week. It was hoped he would be available for this week's game against the Blues in Auckland on Friday night.
Squire would now have to be a long shot to make the All Black World Cup squad. The earliest he will get back is the middle of May when there will be barely a month left in the regular Super Rugby season.
The rugged flanker has played 23 tests since his debut in 2016.
The Highlanders have ready replacements on the blindside flank in the form of Shannon Frizell and Jackson Hemopo and Elliot Dixon is also able to play on the blindside flank.
The Blues will have to do without Sonny Bill Williams this week.
Williams, a Muslim, has headed to Christchurch for the week to help out in the wake of last Friday's tragedy with the permission of his franchise, The New Zealand Herald reported yesterday.