Solskjaer made four changes from the team that lost 2-1 to PSG in the Champions League on Wednesday night, with Fernandes and Rashford only on the bench at the London Stadium.
Dean Henderson replaced David de Gea in goal for Manchester United, while Paul Pogba and Donny van de Beek came in for Fernandes and Fred.
With Rashford on the bench, 19-year-old Mason Greenwood was handed his fifth Premier League start of the season.
Explaining his decision to rest Fernandes and Rashford, Solskjaer said: ‘With Marcus [Rashford] and Bruno [Fernandes], they’re two important players for us. They’ve been kicked between pillar and post lately.
‘Bruno’s [Fernandes] foot has been sore since the Southampton game. The decision was easy to keep him out, hopefully I don’t have to use him tonight.
‘Rashford is fit enough to be on the bench. He said he’s ready if needed.
‘It’s a strong team, we have selection headaches every time. Of course they [the other players] get a chance to prove their worth and show what they can do.’
Manchester United are currently just 10th in the Premier League, one point behind fifth-placed West Ham, who have won their last three matches.
David Moyes has made just one change for the in-form Hammers, with Sebastien Haller leading the line in the absence of the injured Michail Antonio.