Squire suffered the injury against the Cheetahs in early May and while he recovered to join the All Blacks for their series against the British and Irish Lions he did not play in any of the three tests, or for the Highlanders in their 23-22 victory over the tourists.
Fellow All Blacks Aaron and Ben Smith have also been rested for Friday's game at Otago Regional Stadium.
Fullback Ben Smith has been cleared of concussion issues after being forced off during the first Lions match, but tests showed he had an inner ear problem and with the Dunedin-based Highlanders already through to the playoffs, coach Tony Brown chose to give the 31-year-old another week off.
Liam Coltman and Malakai Fekitoa, who were also on All Blacks duty for the Lions series, will play against the struggling Reds.
Fellow All Black Waisake Naholo could be playing his last game in Dunedin for the Highlanders after local media quoted him as saying he was considering a move to the Waikato Chiefs next season to be closer to family.
"I'd like to stay in New Zealand for at least one more year and go from there," Naholo told the New Zealand Herald.
"If I come up to the Chiefs I'll be closer to them and being close to family is important for my rugby career. It helps a lot with many things, but all this time I've been by myself so I don't mind.
"I'm weighing things up at the moment and will hopefully come up with a decision in a few more weeks and see where I go from there.
"I love playing for the 'Landers and the environment with the boys down there makes me enjoy my rugby."
(Reporting by Greg Stutchbury; Editing by Peter Rutherford)
