A "light blow" during Monday's training meant that Victor Nilsson Lindelöf was forced to stand over Tuesday's Champions League match against Atalanta (2-2).
There, United suffered another setback when midfielder Raphaël Varane went out with an injury.
- It is a loss for us that Varane is injured.
We hope that Victor will be ready to play, but I can not promise anything, says Solskjær.
"Very important to us"
After the match in Bergamo, the Swedish defender was praised for his efforts in the United shirt during the season.
- Victor has been very important to us.
He is a very, very important player and a fantastic personality to have.
A guy who is nice to have in the team, Solskjær said at the press conference, according to Fotbollskanalen.
Sweden's national team captain Janne Andersson is certainly keeping his fingers crossed that Lindelöf will be ready to play.
The Swedish team captain has been selected in Blågult's World Cup qualifying squad for the away matches against Georgia and Spain next week - when Sweden can secure a World Cup place.