Officers were alerted to the discovery of a body in Gordon Road, Clifton, by a member of the public and the road was shut shortly after 06:45 BST.
An area around the junction with Queens Road and near to Bristol Students' Union was cordoned off.
Avon and Somerset Police said forensic examinations were carried out at the scene.
Det Supt Carolyn Belafonte said: "We have evidence which suggests the man may have been involved in a collision and we're focussing our inquiry on locating the vehicle involved.
"I'm appealing to anyone who was in the Clifton area in the early hours of this morning, specifically the area around Gordon Road which is close to the Students' Union building, to call us if they saw or heard anything suspicious."
Police are not releasing any more information about the victim until his next of kin have been informed.
A body found in Bristol is that of a man who was killed in an suspected "hit-and-run" collision, police have said.