The Dane had scored seven goals in his last six Premier League appearances after failing to find the net in his first 14 for the club.
Hojlund has been ruled out of Saturday’s clash against Fulham and is expected to miss next weekend’s derby away to Manchester City.
The 20-year-old will also miss United’s FA Cup fifth round tie at Nottingham Forest on February 28.
“Rasmus Hojlund will miss Manchester United’s Premier League game against Fulham on Saturday due to a muscle injury,” United said in a statement.
“It is expected to keep him out for two to three weeks.”
Hojlund has scored 13 times in total in his first season in England after a £64 million ($81 million) move from Atalanta.
His absence is just the latest blow to United’s hopes of qualifying for next season’s Champions League just as they were gaining momentum.
Luke Shaw has suffered a significant hamstring injury that could keep him out for the rest of the season.
Lisandro Martinez is also sidelined for at least another month after suffering knee ligament damage in early February.
United have won their last four league games to climb back into contention for a top-four finish.
Erik ten Hag’s men trail fourth-placed Aston Villa by five points and are just three adrift of Tottenham in fifth.
Five places in next season’s Champions League could be up for grabs in the Premier League should English sides perform well in the latter stages of European competition this season.
The club’s new co-owner Jim Ratcliffe stressed this week the importance of Champions League revenues to allow United to strengthen their squad in the summer without breaching financial fair play controls.
