The broadcaster said in a statement that a power outage earlier on Wednesday morning had caused the SABC's internal systems to switch from City Power to a back-up generator.
"Due to the ageing and failure of the equipment, this led to the diesel tank overflowing," the statement read.
According to a report on News24, employees were evacuated and were told to stay at home on Thursday.
SABC spokesperson Vuyo Mthembu said that Radio 2000, 5FM and Metro FM would continue operating normally as their studios were on the ground floor of the building and were not affected by the spill.
"Contingency plans have been made for other radio stations to broadcast from other locations. For now, nobody will be allowed in [the contaminated] areas."
Mthembu could not estimate when the cleanup would be completed.
In the meantime, City of Johannesburg Emergency Services will remain on the premises until mopping up was completed and the building was declared safe.
Read more on News24.
