She said no crime is suspected in relation to the film maker's death.
"Searching for Sugar Man," which detailed the life and career of American singer Sixto Rodriguez, won the Oscar for best documentary in 2013.
Rodriguez and his family learned of Bendjelloul's death shortly before his home town concert on Tuesday night at Detroit's Masonic Temple Auditorium. He did not mention it from the stage but afterwards told Billboard that, "It's a shock. I just found out about it a couple of hours ago. He was a very talented man and hard-working artist -- he proved it by hitting an Academy Award his first time out. My deepest condolences to his family. Rest in peace."
Bendjelloul grew up in central and southern Sweden and acted in Swedish TV-series "Ebba and Didrik" as a child during the 1990s. He studied journalism and media-production at the Linnaeus University of Kalmar in southern Sweden and later worked as a reporter for Swedish public broadcaster SVT.
He resigned from that job to travel the world and he got the idea for "Searching for Sugar Man" during one of his trips.
Additional reporting by Gary Graff.