According to an Eskom statement, the City of Johannesburg and its power utility, City Power, owed it an arrear debt of R5.26bn. A further R1.58bn rand is due on 5 June.
The City of Johannesburg did not immediately respond to a Reuters request for comment.
Eskom has issued a notice of its intention to "reduce, interrupt and/or terminate the supply of electricity to certain bulk supply points against the City of Johannesburg and City Power".
The utility said it had worked with the Johannesburg metropolitan municipality for more than two years over the unpaid debts, but the city had repeatedly defaulted.
Johannesburg's financial woes have been in the spotlight recently after the country's National Treasury raised "serious concerns" over the state of its finances.
Eskom has also had longstanding financial troubles, but it has started to emerge from them thanks to government bailouts and a sudden turnaround in the performance of its coal-fired power station fleet. It reported its first full-year profit in eight years last year.
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