The England centre-half joins Axel Tuanzebe, Eric Bailly and Marcos Rojo as unavailable central defenders for Saturday's Premier League match against basement club Norwich.
Left-back Luke Shaw is also a doubt, while Solskjaer's decision to allow another international centre-back, Chris Smalling, to move to Roma on a season-long loan now looks seriously flawed.
Solskjaer has taken the precaution of recalling Cameron Borthwick-Jackson from a loan spell with League One side Tranmere.
The manager's problems at the back are compounded by the fact that two of his first-choice midfield players, Paul Pogba and Scott McTominay, are also facing extended spells on the sidelines.
Man United's Maguire an injury doubt for League Cup semi: Solskjaer
United, who suffered a demoralising 3-1 home defeat to Manchester City in the first leg of their League Cup semi-final on Tuesday, are fifth in the Premier League, five points behind fourth-placed Chelsea.
But, with a squad stretched to breaking point, they face a challenging spell of fixtures over the next few weeks, including an FA Cup third-round replay against Wolves before a match at Anfield against league leaders Liverpool.
Saturday's meeting with Daniel Farke's Norwich would appear to give United the ideal platform to rediscover their confidence after the dismal defeat against City.
But their performances against the Premier League's lesser lights this season have been woeful, with defeats against Watford, Bournemouth and West Ham.
A hip injury to Maguire, an £80 million ($105 million) signing from Leicester, leaves United facing the prospect of taking on Norwich with just two fit senior centre-halves -- Victor Lindelof and Phil Jones.
When speaking about Maguire following the defeat by City, Solskjaer had been optimistic the former Leicester player would not be out for long but it appears that is no longer the case.
"We don't know (about Maguire). He's not going to be long term, but I don't think he'll be ready for the weekend, but let's see," Solskjaer had said.
Reports said Maguire, who did not play against City, could be out for several weeks.
Pogba's return to United only positive from Watford loss says Solskjaer
Jones, 27, has struggled for form, fitness and confidence for most of the season, with just one league start to his name and appearances in just six games across all competitions.
The lack of playing time was evident against City, with the defender suffering from cramp late in the tie.
His lack of match sharpness was also cruelly exposed by United's rampant neighbours in midweek and it could be seen as a calculated gamble, or act of desperation, for Solskjaer to start him against Norwich.
Whether Solskjaer is able to bring in suitable reinforcements in January remains to be seen but he is adamant United will only make signings if the right players become available.
"We are a young team and with the injuries we've had and illness it shows more and that's something we are looking at," he said.
"If there is something there for us I've got the backing to do something, but if it is not the right thing we won't do anything."
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