Postbank, the bank jointly owned by An Post and French bank BNP Paribas, has said it plans to wind down by the end of the year.
In a statement, the bank said it would continue until the end of 2010, but not beyond then.
It will not be accepting new banking customers from Monday.
Postbank said customers do not need to take any action at the moment and will be writing to its 200,000 customers in the coming weeks.
Deposits will continue to be covered by the Government's guarantee scheme.
Postbank employs 260 people, but says it hopes a 'significant proportion' of these can be saved, as it hopes some of its financial products could be developed further.
It operates banking, savings and investments, and insurance services in almost 1,000 post offices across the country.
Chairman of the Postbank Board Thierry Schuman a number of factors including the ‘unprecedented circumstances’ in which the financial services sector finds itself contributed to the decision.
The Financial Regulator said it was working with Postbank to ensure that customers' interests were protected in accordance with the Consumer Protection Code.
It pointed out that Postbank's decision did not affect An Post savings accounts, which will continue to operate as normal.
Customers with any concerns or questions about their accounts are advised to contact Postbank directly on 1890-303040 on www.postbank.ie
General Secretary of the Communications Workers Union of Ireland Steve Fitzpatrick described the decision as a missed opportunity to provide banking services to ordinary people through the extensive post office network.
IFA Deputy President Eddie Downey has said the decision to close Postbank is a serious blow to rural Ireland which he said will further reduce important services.