McQueen was born in London and is of Grenadian and Trinidadian descent.
He grew up in Hanwell, West London and went to Drayton Manor High School. In a 2014 interview, McQueen stated that he had a very bad experience in school, where he had been placed into a class for students believed best suited "for manual labour, more plumbers and builders, stuff like that." Later, the new head of the school would admit that there had been "institutional" racism at the time. McQueen added that he was dyslexic and had to wear an eyepatch because of a lazy eye, and reflected this may be why he was "put to one side very quickly".
He was a keen football player, turning out for the St. George's Colts football team. He took A level art at Ealing, Hammersmith and West London College, then studied art and design at Chelsea College of Arts and then fine art at Goldsmiths College, University of London, where he first became interested in film. He left Goldsmiths and studied briefly at New York University's Tisch School of the Arts in the United States. He found the approach there too stifling and insufficiently experimental, complaining that "they wouldn't let you throw the camera up in the air". His artistic influences include Andy Warhol, Sergei Eisenstein, Dziga Vertov, Jean Vigo, Buster Keaton, Carl Theodor Dreyer, Robert Bresson, and Billy Wilder.