Ivorian centre-back Bailly, a close-season signing from Villarreal, limped off early in the second half at Stamford Bridge, with Marcos Rojo coming on to take his place.
"He is injured and I'm afraid he's badly injured," Mourinho said in his post-match press conference.
"In his knee, in the ligament area, he feels that is really bad."
Bailly, 22, joined United from Spanish side Villarreal in June for a reported fee of 30 million pounds ($36.7 million, 33.7 million euros).
The Ivory Coast international has been a virtual ever-present to date this season, starting all 12 of United's Premier League and Europa League games and only sitting out a League Cup tie.