Postbank, the banking arm of An Post, is winding up its operations at the end of year.
The group has blamed "unprecedented circumstances within the financial services sector" for the move.
It is set to write to customers in the coming weeks to advise them of their options.
Postbank says it hopes to secure jobs for some of its 260 employees around the country through the development of new products and services.
"Postbank Ireland Ltd (a joint venture between An Post and BNP Paribas Fortis) has informed the Financial Regulator of its intention to wind down its business by the end of 2010," said a statement from the company.
"This is a commercial decision and Postbank’s joint venture shareholders have committed to fully support the bank throughout this period.
"The Financial Regulator is working with Postbank to ensure the orderly management of the process and that customers’ interests are protected in accordance with the statutory Consumer Protection Code.
"Postbank will be contacting all customers about their options and has advised that customers will be able to conduct their banking, insurance and related Postbank activities in the normal way.
"Postbank’s deposits are guaranteed under the Government Guarantee and Deposit Protection Schemes.
"This decision does not affect An Post savings accounts which will continue to operate as normal."