The England international hobbled off just before half-time in Sunday’s 2-1 Premier League victory at Luton.
The 28-year-old now faces a race against time to prove his fitness to make the England squad for Euro 2024.
“Luke Shaw has sustained a muscle injury and will be out for an extended period,” United said in a statement on Wednesday.
“Further assessment is still required to determine the severity but we expect him to be absent for a few months.”
Shaw, who has made just 15 appearances in all competitions in an injury-interrupted season, had only returned to action in January after a month out.
United are short on cover at left-back as Tyrell Malacia has been sidelined all season and the club opted to cut short Sergio Reguilon’s loan from Tottenham in January.
