Tuesday's 2-1 loss against former club Leicester saw the 28-year-old miss his first Premier League match since joining the club in a world record deal for a defender in 2019.
Maguire watched from the stands with crutches and his left foot in a boot after finding out he had sustained ligament damage when Aston Villa's Anwar El Ghazi awkwardly landed on him on Sunday.
Solskjaer expects the defender to miss the remaining Premier League matches against Liverpool, Fulham and Wolves, but retains hopes that he could be fit to face Villarreal in the Europa League final on May 26.
"The good news is it wasn't broken, there was no fracture, but a ligament injury, of course, is serious as well," the United boss said.
"If I'm very positive... that's maybe stretching it, I'm hopeful he might be ready for it.
"I don't think he'll play in the league again before but we'll do everything we can to get him ready for the final."
Maguire's injury is a concern for country as well as club, with Gareth Southgate naming England's European Championship squad the day before the Europa League final.
"You always try to look after players long-term," Solskjaer said. "If he's fit, he'll play for us. If he's not, he won't.
The 34-year-old had been ready to leave after one campaign and return to South America, but the in-form frontman has now committed to the 2021/22 campaign.
"I think we've seen the last few months what we can expect and what we wanted from him," Solskjaer said.
"Next season he'll come ready. He'll be fit when he comes in pre-season. This year he had seven months of no football to catch up and that's not easy and he's had a couple of niggles because of that.
"Just the same, professionality, he comes in every day, does everything right. The boys will look at him.
"He gives us a number nine position. I don't know how many games we'll get out of him but he's one of the best number nines in the world at the moment."