The matter is under investigation by the Data Protection Commissioner.
Electric Ireland says Gardaí and the Data Protection Commissioner, Athlone's Helen Dixon, are investigating the compromising of around 8,000 customer accounts.
It says it's aware an employee working on its behalf may have inappropriately accessed some customer accounts, leading to the potential misuse of personal and financial information.
All customers who may have been impacted have been written to, and only those who have received a letter need to take action.
Electric Ireland says it fully appreciates the gravity of this issue and the concern and inconvenience it will create for those affected.