The company says it will test the meters and refund any money which was overcharged.
The affected electricity meters were installed mainly in apartment blocks around the country from 2007 onwards.
27,000 customers have been written to and informed that their meters will be replaced and tested, but ESB Networks is primarily concerned with a batch of around 17,000 meters.
It estimates that around 10% of these could be faulty.
The fault is thought to be caused by deterioration in one of the components which causes the meter to over-record, before it stops working.
This can result in some customers being incorrectly charged.
ESB Networks said it will be able to determine from tests whether customers have been wrongly billed and will refund any money overcharged.
The company said in a statement: “ESB Networks advises all customers that they do not have to take any action with their meters.
“ESB Networks will contact all affected customers and test the meters.”
Speaking on RTÉ’s Morning Ireland, ESB Networks spokesperson Bernadine Maloney said: “The meter typically over records and then fails. It’s important to note that customers won’t lose their supply, the meter just stops reading and there’s no safety issue at all.”
Sinn Féin TD John Brady said he has asked Minister for Communications Denis Naughten to ensure that a procedure for repayments is put in place as swiftly as possible.