West Ham warn McCarthy over weight
The 32-year-old joined the club from Blackburn Rovers in January but his weight problems cost him a place in South Africa's World Cup squad in June.
Now West Ham have lost patience with him, Sullivan telling the Daily Telegraph newspaper: "Benni has been given a serious weight-loss programme and if he doesn't lose the weight we will be fining him.
"We are not being unrealistic. We've given him a target of losing a kilo (2.2 pounds) a week. He has to lose five or six more kilos.
"He is training very hard so he must be eating or drinking something very wrong. Short of spending 24 hours with him, we have to assume that."
West Ham, with new manager Avram Grant in charge for the first time, start the Premier League season with a visit to Aston Villa on Saturday and McCarthy is unlikely to be included in the team.
"It's like a jockey turning up overweight. He can't ride a horse and no one is going to pay him. I think we are fully within our rights to say 'you are not honouring your side of the contract'," added Sullivan.
"You expect him to turn up in a state to be a footballer. We are not starving him. It's just don't eat ice cream, don't eat cakes, don't drink wine."