Emergency services arrived at the Davidson Street building in Bellfield, in the city's  northeast, shortly before 11.30am on Wednesday.
The man, who police are yet to identify, was declared dead at the scene, with investigators looking into the circumstances of the death.
Homicide detectives are questioning a 54-year-old man arrested nearby.
Police have told AAP they are unable to comment on reports officers had examined a knife or hammer to determine if that was used in the incident, or that officers were called to a disturbance late on Tuesday evening.
A neighbour said she heard cries and screams from the apartment about 11.30pm on Tuesday.
"It was shrills over a period of maybe 10 minutes," the neighbour told television news crews.
"There was a police car outside last night, that I saw, so I thought it had been dealt with, but then this morning we heard more sobbing.
"To me it sounded like the same voice that I heard crying last night and screaming last night to what I heard this morning."
Officers have taped off a toilet block near the scene.
They have urged any witnesses or anyone with information or CCTV footage to contact Crime Stoppers.
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