The defender suffered a hamstring injury during Saturday’s 3-1 home defeat to Brighton after coming on in the 85th minute.
Wan-Bissaka is expected to be sidelined until November at the earliest, with further reports claiming the defender faces two months out.
The 25-year-old started the game on the bench after battling with illness earlier in the week.
Wan-Bissaka’s setback adds to a growing list of injuries at United, with midfielder Mason Mount and defenders Luke Shaw and Raphael Varane also sidelined in recent weeks.
Brazilian forward Antony has been given in indefinite leave of absence to address assault allegations made by former girlfriends
United have lost three of their last four games and next travel to Germany to face Bayern Munich in their opening Champions League Group A game on Wednesday, before visiting Burnley in a Premier League clash on Saturday.