Gateshead Council said it is not known how many residents have been affected by the attack, which happened in the early hours of 8 January.
Officials at the authority have advised people to watch out for phishing emails or fraudulent activity, and to change passwords if they are concerned about suspicious activity.
The council said it would contact people impacted by the data loss, adding that the threat had been “quickly contained”.
The attack is being investigated by the North East Regional Crime Unit, the Local Democracy Reporting Service said.
Gateshead Council’s strategic director for corporate services and governance, Mike Barker, warned residents to be “vigilant for anything that does not seem right, and be cautious when sharing your personal information”.
“As investigations continue there is a possibility of further issues arising, and we will work to mitigate this should that be the case,” he continued.
Mr Barker added: “Investigations so far have not indicated there is any further damage caused, but we need to be open to the possibility.”
Gateshead Council said it was taking the breach “extremely seriously”, while asserting “robust security measures have meant the potential damage this could have caused has been mitigated, and we are still able to operate our day-to-day business activities”.
“Incidents of this nature, unfortunately, are on the rise – with many organisations like ours already having dealt with such situations,” Mr Barker said.
