Shaw, who this season returned from a double leg break, had worked his way back into Jose Mourinho's thoughts in recent weeks, only to be forced off early in United's 1-1 home draw against Swansea on Sunday.
The United boss said it must have been a "big injury" to go off so early and Press Association Sport understands the left-back will see a specialist after scans on Monday showed ligament damage in his left foot.
Shaw's setback is a big blow on both individual and collective levels as the season comes to a head. The United left-back has had to deal with issues related to his long injury lay-off this term and has struggled for game time under Mourinho.
The Portuguese has publicly questioned the England international on several occasions, but a meeting between the pair last month led to a surprise first-team return.
Sunday's match against Swansea was Shaw's fourth United appearance of April, but came to an end after just nine minutes.
He joins Mourinho's injury list at a crucial time in the campaign as United look to finish in the top four and win the Europa League.