According to an official from the Sanyogitaganj police station, the unclaimed body was found lying at the entrance of the hospital last night.
The identity, the cause and time of his death are yet to be ascertained, the police said.
It is also not known whether the young man was undergoing treatment at the hospital.
When contacted, Hospital Superintendent, Dr VS Paul, said he had no information on the man and the police is probing the matter.
The body has been sent for autopsy, he said.
This was not the first such incident in Indore.
In June last year, a similar matter was reported from a district hospital when ants preyed upon the corpse of a three-day-old baby girl, awaiting post-mortem in the mortuary.
She had died due to alleged negligence of the hospital staff.