The 24-year-old suffered a injury following a challenge by Fulham striker Erik Nevland in Sunday’s 1-0 defeat at Craven Cottage.
Bruce told the Sunderland Echo: “It’s a nasty one for Anton.
“Nevland’s body weight came down on the ankle when they went to ground and he’s no chance of being ready for the weekend.
“He’s got no chance for Saturday and it looks like it could be a month at least for him.
“It’s disappointing for him and disappointing for me.”