The left-back tested positive earlier this week, and while he is showing no symptoms he will not be able to compete against the Gunners on Sunday.
The 27-year-old has still made just one appearance for the Red Devils, in the impressive victory away to Paris Saint-Germain in the Champions League, and he will have to wait to wait for his Premier League now.
Eric Bailly, Jesse Lingard, Phil Jones and Sergio Romero were already out, while Anthony Martial is still suspended, but otherwise Solskjaer is happy with the options available to him.
‘Alex won’t be ready, no,’ Solskjaer told a press conference on Friday. ‘Apart from that I would think everyone else, at the moment, looks like they could be involved.
‘[The squad looks] good. There was no injuries [from Wednesday] which of course is a big plus when you think of every game we play and the intensity. We’re getting better and better, I think everyone is seeing now that our fitness and sharpness is more up to speed and we should be ready for that game [on Sunday].’
Adding on the situations of Romero and Jones, neither of whom have been involved this season, the Norwegian said: ‘Sergio has just come back into training this week. He’s started his pre-season work and he’s working to get to his peak fitness with the goalkeepers.
‘Phil has been injured and he had an operation and he’s been working really hard to get back. He’ll hopefully get fit during December. That was a natural thing when you’re injured, you can’t really be in the squad can you? He’s working really diligently and he’ll be coming back soon.’
The Brazil international was keen to stress that he was feeling fine and will be back and ready to play imminently.
‘Guys, I want to thank you for the messages of affection that I received from the moment that United announced that I have been diagnosed with COVID-19,’ Telles wrote on social media.
‘I want to say that I am fine, isolated and soon I will be back with all my strength to help my teammates. Once again, thank you all for your lovely messages!’
United host Arsenal at 4.30pm on Sunday as both look to find some consistency in the Premier League and build on positive results in Europe in midweek.