Fassbender went on a medically-supervised diet to play Sands
Artist Steve McQueen has won a prize at the Venice Film Festival for his film Hunger, about IRA hunger striker Bobby Sands' final days in the Maze prison.
McQueen was awarded the Gucci Group Award - which honours film-makers from other fields.
The film, directed by McQueen, stars Michael Fassbender as Sands, who died in 1981 at the Northern Ireland jail at the age of 27.
The film also won the Camera d'Or prize at the Cannes Film Festival in May.
"We're living in a time and age where it is all about putting our cards on the table and going for it," McQueen said as he accepted his award at a ceremony at the Palazzo Grassi.
Actor Fassbender went on a medically-supervised diet to play Sands who refused food for 66 days in an attempt to be recognised as a political prisoner.
McQueen told the BBC earlier this year he had been inspired by his memory of seeing Sands on TV news bulletins as an 11-year-old.
Fassbender and McQueen launched the film in Cannes earlier this year
McQueen, who won the Turner Prize in 1999 for a collection of films including a silent movie stunt, beat fellow Brit nominee Isaac Julien.
London-based photographer Julien was nominated for directing Derek - a film about late director Derek Jarman - written and narrated by actress Tilda Swinton.
Adam Yauch, of hip-hop outfit the Beastie Boys, was also nominated for directing Gunnin' for that No1 Spot, a documentary about high school basketball players.
And artist Julian Schnabel, who won the award last year, was nominated again for directing Berlin - the film of singer Lou Reed performing his concept album of the same name.