Valencia, who has worn the captain's armband this season in the absence of Michael Carrick, was forced off with a muscular problem in the second half of last weekend's 2-1 win over Tottenham Hotspur in the semi-finals of the FA Cup.
The Ecuador international had been seen as a doubt for the clash with the Gunners this weekend, but Mourinho has confirmed that apart from second-choice goalkeeper Sergio Romero, he has a fully-fit squad to choose from.
"Everybody's fine," Mourinho told MUTV. "I have 22 players and apart from Romero as a goalkeeper, everyone is fit to play."
United will face Arsenal, Brighton & Hove Albion, West Ham United and Watford in their final four Premier League matches of the season before taking on Chelsea in the FA Cup final on May 19.