"We've just attended to an incident in Yeoville, at Sanders Mansion, a block of flats," spokesperson Robert Mulaudzi said.
"A man in his 30s jumped from the fifth floor and unfortunately he lost his life."
The man died of multiple injuries.
"Police are on the scene. The cause of his jump is still unknown but the relevant authorities are investigating," Mulaudzi said.
"It is believed at this stage that the man jumped."
This was at least the third incident of someone jumping from a building in central Johannesburg this month.
"We just want to advise people to refrain from doing so," said Mulaudzi.
"If there are any issues which one needs to deal with, they can contact the relevant NGOs and organisations that help people in distress."