He was 36.
Police have yet to specify the cause of death, though officials do not suspect foul play.
The Swedish-born filmmaker started out as a child actor, but went on to produce short documentaries about musicians for Swedish public television.
Bendjelloul is best known for Sugar Man, the story of reclusive and mysterious American folk musician Sixto Rodriguez, which won the Oscar award for best documentary feature in 2013. It opened the Sundance Film Festival in 2012 and won the coveted Audience Award.
Rodriguez never made it in his native country, but became an huge success in South Africa. The film documents two fans' attempts to locate him.
"It's not just a random story,'" Bendjelloul told THR last year. "I retold the story to friends, and they were like, 'This is the best story we've ever heard. It's like a fairy tale.'"