Unit two's automatic protection mechanism tripped around 2.40pm, shutting the unit down and taking it off line, Eskom spokesperson Fani Zulu said.
The cause had not yet been established and was being investigated, he said.
This meant both units at the power station were now off line.
Unit one was shut down on 26 January for long-term planned maintenance and was expected to come back on line early in May.
Zulu said there was "some degree of comfort on our part that we can survive" this unplanned shutdown of unit two without interruptions in the power supply to the Cape.
Eskom had recently doubled the output of the two new gas turbine generators in Atlantis and Mosselbay, and they were now an important part of managing this period.
The most important differentiator now was how consumers in the Cape used electricity during this period. Past experience had shown consumers could reduce their consumption when both Koeberg units were out.
Zulu appealed to consumers to conserve electricity.
Sapa
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