The Italian, who moved to the Stadium of Light as Martin O'Neill's replacement last week, has admitted that he will take a hard stance on anyone drinking alcohol throughout the week.
"If I discovered one of my players had drunk not on a Friday but even a Monday night, I would fine him," Di Canio told the Sunderland Echo.
"If you are talking about a glass of red wine during dinner with family on a Monday night or Tuesday night, that's good because we know red wine is good for the heart.
"But forget about alcohol on Thursday or Friday. I don't think this team have this habit, I hope not."
Di Canio suffered a 2-1 defeat to Chelsea during his first game in charge of the Black Cats.