Bailly was forced to leave the field on the hour mark during the 1-1 draw with Swansea following a challenge with Fernando Llorente and was unable to continue.
The Ivory Coast defender was pictured by a fan leaving the ground wearing flip flops and his right ankle strapped as he slowly made his way towards his car.
Bailly is unlikely to be fit for the crucial Europa League semi final clash against Celta Vigo on Thursday night.
Bailly, 22, became United’s fourth and final senior centre half to succumb to injury within a five-week period, leaving Jose Mourinho with 19-year-old Axel Tuanzebe as his only specialist centre-back.
Matteo Darmian emerged instead of Tuanzebe to replace Bailly and Mourinho spoke about his latest selection dilemma for the Celta fixture.
“I know that the players I choose will give everything,” Mourinho said. “So it doesn’t matter if I go with Darmian central defender, if I go with Carrick or Axel, I trust the boys.
“The spirit is amazing, the group is phenomenal, Fellaini and Pogba will be back for that game, so a bit more options and we try with everything we have and we go again.
“We lost players and we lost points, so yes today was a bad day. We did not look tired and exhausted, we are tired and exhausted. You cannot isolate the performance out of the context. This is the ninth match of April, it is not human.
“We have a squad of 22 that is reduced to 13 or 14 players. The players are very tired.”
Bailly was the only United player who started all nine of their matches in April and was outstanding in the games against Chelsea, Burnley and City.
Paul Pogba is due to return to the squad for the Celta match and Marouane Fellaini will also be available since his suspension applies to domestic matches.
United seem set to be without Phil Jones, Chris Smalling, Marcos Rojo, Zlatan Ibrahimovic, Timothy Fosu-Mensah, Luke Shaw and Bailly, though.