The actor had to go on a medically-supervised diet to portray Sands, who refused food for 66 days in the Maze prison in a bid to be recognised as a political prisoner.
The film does not yet have a UK release date.
An earlier film on Sands' life, Some Mother's Son, caused controversy when it screened in Cannes in 1996.
Director McQueen, who won the Turner Prize in 1999 for a collection of films which included a Buster Keaton-style silent movie stunt, told the BBC earlier this month he was inspired by the memory of seeing Sands on TV news bulletins when he was 11.
"There was this man called Bobby Sands whose image appeared on TV with a number underneath it," he recalled.
One scene features a conversation between Sands and a Catholic priest about the decision to go on hunger strike.
Filmed in one continuous 10-minute take, it was shot on the first day of filming in Northern Ireland and took Fassbender and co-star Liam Cunningham four attempts to complete.
Hunger was co-written by Irish playwright Enda Walsh and co-funded by Northern Ireland Screen and the Broadcasting Commission of Ireland.
The Irish government's arts minister Martin Cullen said it was the third year in a row that an Irish-backed film had been successful at Cannes.
He added: "Following the success of The Wind that Shakes the Barley and Garage, this Camera D'Or will keep Irish film practitioners in the world's eye for the foreseeable future.
"This film covers a very turbulent part of our history with an unadorned reality and reminds us of how far we have come as an island in the last quarter century."
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