The Denmark international capped his first appearance of the summer with a goal, sending Man United ahead in their friendly with Mikel Arteta's side, but he had to be replaced soon after after picking up an apparent hamstring issue.
The 20-time English champions have not provided an update on the centre-forward's fitness ahead of Wednesday night's pre-season clash with Real Betis.
According to The Sun, Hojlund is unlikely to face the Spanish outfit, but there is a chance that he could be fit for Saturday's game against Liverpool, with the 21-year-old only suffering a minor issue.
Hojlund is therefore expected to be available for the Community Shield against Manchester City on August 10, with that match coming six days before the team's opening game of the new Premier League season against Fulham.
Hojlund only suffered 'a minor pull' against Arsenal
The Dane scored 16 goals and registered two assists in 43 appearances for Man United last season following his arrival from Atalanta BC.
Hojlund is again set to be Man United's starting striker in the new season, having been handed the number nine shirt following Anthony Martial's exit.
However, Joshua Zirkzee has been signed to boost Erik ten Hag's attacking options, and the recent arrival could make his debut against Man City.
While Man United have allegedly received good news on Hojlund, the same is not believed to be true when it comes to Leny Yoro, who also had to be substituted in the first half of the game with Arsenal.
How long will Yoro be out?
Yoro has allegedly damaged his metatarsal, which could rule him out of the team's opening three matches of the new Premier League campaign.
The 18-year-old is also set to miss the Community Shield, with his first competitive appearance for his new club potentially coming against Southampton on September 14.
As well as the Premier League opener with Fulham, Yoro is set to be sidelined against both Brighton & Hove Albion and Liverpool in the league.
Kobbie Mainoo and Amad Diallo are two players to have suffered serious injuries during the team's pre-season preparations last summer; Ten Hag will now be hoping that his team do not pick up any further fitness problems in their next two friendly fixtures.