“It looks like the man succumbed to smoke inhalation and died inside the building,” said spokesman Robert Mulaudzi.
The man was declared dead on the scene in a building on corner Rissik and Loveday.
The injured people were treated on the scene before they were taken to hospital, he said.
One was burned and injured, the other one was injured while rushing out of the building.
Mulaudzi appealed to communities within the city of Johannesburg to look after their heating and lighting appliances which might cause fire if unattended.
On Monday, a fire swept through five shops along Bree and Mooi streets.
Four shop were also burned on Wednesday in a building on Eloff and Plein streets.
“It is a matter of concern to us as the authorities since this is the third fire incident in the CBD this week.”