News reports said the incident happened at the Island View terminal and that three tanks containing highly flammable liquids exploded at 7 pm local time.
Two of the tanks contained solvents and the third contained lubricant oil, it was reported.
Kobus Ehlers, managing director of Island View Storage, said he did not know what had caused the fire.
''Obviously forensic investigations will be conducted to determine what caused all of this,'' he said.
The fumes from the fire should not pose major health threats, he added.
Firefighters allowed the tanks to burn-out due to the intensity and strength of the fire.
Ships at Island View berths were evacuated as a safety precaution.
Police cordoned off all roads in the area, re-routing trucks heading for the Durban container terminal.