The issue is still being assessed but the left back had been ruled out of “forthcoming games”, it added.
Shaw, 28, has been a mainstay in manager Erik ten Hag’s squad and started United’s first two league games – a 1-0 win over Wolverhampton Wanderers and a 2-0 defeat at Tottenham Hotspur.
United host Nottingham Forest on Saturday and travel to last year’s runners-up Arsenal next weekend before the international break.
Midfielder Mason Mount has already been ruled out of both games after sustaining an injury during their 2-0 loss to Spurs. Back-up left back Tyrell Malacia is also sidelined due to an injury sustained last season.
(Reporting by Hritika Sharma in Hyderabad; Editing by Peter Rutherford)