The body was discovered Tuesday after a neighbour heard cries from the apartment in the northeastern 19th arrondissement, and later noticed blood in the hallway.
The victim was neither the tenant nor the owner of the apartment, a police source told AFP.
According to Le Parisien newspaper, the man was found lying on the floor with holes in his feet and stomach. Investigators suspected some of the wounds may have been inflicted with a drill.
He had also suffered several blows, including to the head, the newspaper said.
The victim was of Asian origin and his identity has not been released.