The England international suffered a stress fracture in his back during a substitute appearance against Wolves in the FA Cup on Jan 15.
It has been suggested the injury was already pronounced enough to question whether his involvement in the cup tie was justifiable and Solksjaer has come under heavy criticism for using a player he knew was injured and who only lasted 16 minutes.
Speaking after United’s 2-0 defeat to Liverpool at Anfield on Sunday (Jan 19), Solskjaer said Rashford’s absence, allied to long-term injuries for midfielders Paul Pogba and Scott McTominay, may force the club into action in the two weeks before the transfer window closes.
The Red Devils have been strongly linked with a move for Sporting Lisbon midfielder Bruno Fernandes.
“The permanent signings we are looking for, those targets are not going to change because we’ve got players injured for the next two or three months,” said Solskjaer. “There might be some short-term deals we have to do.”
Rashford's absence is a huge blow to United's hopes of challenging for a top-four finish in the Premier League and in three cup competitions.
The 22-year-old has netted 19 times in his best ever goalscoring season and is not expected back until after the March international break.
“He’s suffered a bad injury,” added Solskjaer.
“It will probably be six weeks before you can get going and then he's got to get match fit.
“It happened against Wolverhampton and it is not something that has happened before. I’m looking at Marcus to be out for a while. He won’t be back, I'm not a doctor so I don't know exactly, but we are looking at several weeks and then some rehab after that probably.
“We’ve had many injuries to big players this season, it’s just an unfortunate position that we are in. The window is open and it might be that we look at something for the short term.”
‘Blink and I’ll be back’
The player himself has vowed to return for “fitter than ever.”
Rashford tweeted: “Blink and I'll be back, fitter than ever. See you soon.”
The England international also said he would remain heavily involved in all aspects of club life at Old Trafford during his rehabilitation.
“On the pitch or not, @ManUtd fans don't get much bigger than me,” he added.
“You best believe I’ll be involved in team meetings, team huddles and team sessions throughout this recovery.”
News of Rashford's injury is also another concern for England manager Gareth Southgate with Euro 2020 on the horizon.
The Three Lions already have an injury doubt over captain Harry Kane, who has undergone surgery on a hamstring tear and will be sidelined until at least April.