Those on site noticed a blaze around 15:00 and rushed out of the building. No injuries were reported.
"The blaze seems to have gutted an unused garage that is situated at the premises. The premier was not there. He is at the ANC's policy conference [in Johannesburg]," Mbananga said.
He said reports that a carwash on the premises could have been a possible cause were incorrect, as there was no such business situated there. "Firefighters must be allowed and given the space to conduct their investigations and determine the extent and cause of the damage."
Authorities were going through the structure to ensure the blaze was contained and put out. They also wanted to make sure everyone was out.
Mbananga said the structure that caught alight was part of an administrative building housing the director-general and other units. The legislature was next to that. The premier's actual office was about 1.5km away.
Earlier on Friday, the finance offices of the Gauteng Premier's department were destroyed in a fire. The apparent cause was an electrical fault.
Almost 300 staff members were evacuated from the offices and no injuries were reported.
Mbananga would not speculate on whether the fires were linked. "That is for investigators to decide. If the two events are linked, law enforcement [officers] are more than capable of dealing with foul play." -– News24