The video game is set in a school with the player taking on the role of a bully. Advance screenshots show three uniformed pupils fighting. One of them can be seen kicking a classmate in the back, while a third looks on with his fists clenched.
Mr Foster believes the game could glamourise bullying and lead to incidents in local schools,
The game is due to be released by Rockstar Games. The company has already courted controversy with its Grand Theft Auto series, which features drive-by shootings, and Manhunt, which features mask clad chainsaw wielding thugs.
Calls for the ban are being led by Leicester MP Keith Vaz.
Michael Foster said: "I know from my constituents how harmful bullying is and what pain it causes young people. This game allows the person playing it to take on the persona of a bully, able for instance to kick and punch other pupils and spit in their food. I think that can only encourage young people to find pleasure and excitement in abusing others."
Liz Carnell, director of the charity Bullying Online, said: "Our view is that bullying is not a joke. It is not a suitable subject for computer games."
Giving Bully an 18-rating would not stop children, she said.
A Rockstar Games spokesman said: "We support and admire the groups who are working hard to address the long-standing problem of bullying. We all have different opinions about art and entertainment, but everyone agrees that real-life school violence is a serious issue which lacks easy answers.
"Bully is still a work-in-progress, but when it's finished we believe most people will agree it offers an exciting experience and tells an engaging story.
"More and more people are beginning to recognise the stories in video games have as many themes and plotlines as books and movies.
"Just as books aren't judged by their covers, video games shouldn't be judged by their titles or individual scenes." The game would be "submitted to the appropriate bodies" to be rated, he added.
Roger Bennett, director general of the Entertainment and Leisure Software Publishers Association, said: "As Mr Vaz knows, any game can be automatically referred to the BBFC for a rating.
"It is disingenuous to suggest any game be banned when the content has yet to be finalised.
"Every game published in the UK carries an age rating on the box, providing guidance to ensure consumers can make informed choices when buying games."
Mr Foster said: "I understand the company has suggested the game might have an 18 rating but we all know this does not stop children accessing them. I really hope we can take action against this kind of irresponsible game. As a society we should be encouraging children to be compassionate and understanding towards others, not glamourising bullying."