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The England centre-back, who has made 39 appearances in all competitions since joining from Leicester City last summer, was left out of Thursday's FA Cup fifth-round clash with Derby County after hurting himself in training.
And Solskjaer confirmed that he is a doubt for the derby meeting with their local rivals at Old Trafford at the weekend.
"I had a word with him before training yesterday to say I'm not going to rest him," Solskjaer told MUTV when asked why Maguire was missing from the team to face Phillip Cocu's side.
"But then he rolled his ankle in training so he had to stay at home. Hopefully he'll be okay for the weekend but I'm not sure."
Maguire, who turned 27 on the day of the Derby clash, took to Twitter to express his disappointment at being forced to miss the encounter with the Championship side and hopes to be back soon.
"Disappointed to miss out through injury," he Tweeted. "Working hard to get fit ASAP. Good luck to the lads."
Victor Lindelof and Eric Bailly started in the heart of the Red Devils defence against Derby as Solskjaer made sixl changes to his team.
Aaron Wan-Bissaka and Daniel James are also in danger of missing the Manchester derby, and Solskjaer urged the rest of the squad to step up and make a claim for a place in Sunday's starting 11.
"Well the players are desperate to play and we wanted to give them a chance. There are a couple of injuries and they couldn't have played anyway. But we've picked a strong team and hopefully we can go through," he added.
"There are a couple of players who are getting the chance to stake a claim for the derby because I'm not sure if Harry, Dan or Aaron are going to be available. So there are chances [tonight] for a few."
United are currently fifth in the Premier League - 15 points behind second-placed City and a further 22 adrift of leaders Liverpool.