Daniel James will miss United's Europa League opener against FC Astana after picking up an injury against Leicester City at the weekend.
The Wales winger has been one of United's star men this season but he hasn't trained ahead of the first European game of the season after picking up a knock in the Premier League victory.
James was withdrawn in the 89th minute against the Foxes, with Axel Tuanzebe coming on, in what was thought to be a tactical substitution at the time.
Luke Shaw, Paul Pogba and Anthony Martial all missed the 1-0 win on Saturday and they won't be available to face the Kazakhstan champions at Old Trafford.
"He (Daniel James) got a knock against Leicester. So he won't be available," Solskjaer said. "Luke, Paul and Anthony [are still out]."
There is good news on the fitness front for United though, with Diogo Dalot and Jesse Lingard both back in training ahead of Thursday's game.
Dalot has been absent since before the international break, while Lingard returned to United from England duty with a bout of flu and missed the game at the weekend.
"Diogo is back, Jesse is back available," Solskjaer said. "We are getting some back and losing some, that's the way it goes."
