It was thought that the saboteurs were workers who embarked on an unprotected strike on Wednesday, City Power said in a statement.
One substation appeared to have been tampered with and at another the power equipment appeared to have been manually put down.
The police were investigating and security guards had been appointed to watch the stations, said City Power.
It was using contractors to try and fix the problem, and power had been restored to parts of Hursthill, Mayfair, Alexandra, Auckland Park and Craighall.
However, it could take up to three days to fix the problems in other areas, City Power said.
Meanwhile, the company obtained a court interdict compelling striking workers to return to work.
City Power said a few hundred disgruntled workers had gone on strike because they were unhappy about a new shift structure being implemented.
It said the strike was not union-led, and that the unions signed an agreement to the new shifts in May.