"I think they will be out for two to three weeks looking at it now," Solskjaer told a news conference ahead of Monday's FA Cup fifth-round clash against holders Chelsea.
The injury comes as a setback for United, who have won 10 out of their 12 matches under caretaker boss Solskjaer, but it provides an opportunity for forwards Alexis Sanchez and Romelu Lukaku to rediscover their goalscoring touch.
Solskjaer said it also opens doors for attacking youngsters Angel Gomes and Tahith Chong, who have been pushing for first-team action this season.
"It is a chance for anyone who plays, whether it is Alexis, Romelu or Angel (Gomes)," the Norwegian coach added.
"Anthony and Jesse have done really well for us, they're vital, but then again with Rom and Alexis, they've got different skill sets and will be able to show what they can do.
"We still have forward options but Angel and Chongy have been training with us all week, even the weeks leading up to this, so there is a big chance they will be involved."
United are also locked in a battle for a top four Premier League finish with Arsenal and Chelsea, and face title contenders Liverpool at Old Trafford on Feb. 24.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
