With three league goals this season, Welshman James is United's leading scorer alongside Marcus Rashford but the 21-year-old has joined team mates Paul Pogba (ankle), Anthony Martial and Luke Shaw (both thigh) on the treatment table.
"He got a knock against Leicester. So he won't be available," Solskjaer told reporters.
"I don't think we'll see Paul or Anthony, I'm sure we won't see them. Luke is not ready yet.
"Diogo [Dalot] is back. Jesse [Lingard] is back, which is great. He had a bad time when he was with England but, hopefully, we'll get him on the pitch to try to kick-start his season again."
Solskjaer confirmed goalkeeper Sergio Romero would play instead of David De Gea, who this week penned a new deal that will keep him at the club until at least 2023.
"Obviously David signed his contract and now we've got him maybe we should keep on playing him," Solskjaer said.
"Sergio will play tomorrow for sure, he's proven to be a top keeper behind David and (we must) keep him ready for if something happens to David. Time for him to have some much needed game time."
Mason Greenwood and Axel Tuanzebe are also set to make the starting lineup as Solskjaer opts for youth while midfielder Fred, 26, is set to make his first start of the season after coming on in the second half of the 1-0 win over Leicester.
"Fred came on well, we needed his legs and sharpness," Solskjaer added. "He's been patient... been working hard.
"He's not a young boy, but he is young in his English career. I'm sure we will see more and more of him, he's had some great games in midfield so we're just waiting.
"Greenwood will play definitely. Axel is one who didn't make the starting XI so now it is a chance for them to get some minutes. There will be some young ones tomorrow."