A group, which identified itself as the Shadow Kill Hackers, left a note on the Twitter page claiming to "have control of everything" in Johannesburg, ZDNet reported.
"All your servers and data have been hacked. We have dozens of back doors to your city. We have control of everything in your city. We also compromised all passwords and sensitive data, such as finance and personal population information," it said.
Another group of hackers is threatening to release Johannesburg customer information if it is not paid four Bitcoins by Monday. It's threatening to launch a 'distributed denial of service' (DDoS) attack.
Several South African banks were hit by cyber attacks and their services went down. Standard Bank and Absa were two of the five banks attacked by what appeared to be DDoS.
Initially, the attacks were reported as coming from the same group, but Shadow Kill Hackers said they were not involved in these unrelated attacks.
The incident is being investigated by security experts, who are striving to limit the impact.
City of Johannesburg spokesman Nthatisi Modingoane said some customer service centres were now running and the remaining services would be back by the end of weekend.
Earlier in July, Johannesburg's power supply was hit by a virus that restricted customers' online buying of electricity.
( With inputs from IANS )