The bank is shutting its retail operation here, but will give those with credit card accounts a month longer to clear their balances and find a new card provider, the Irish Independent has learnt.
Danske Bank said in October it was winding up its business and personal banking operations with the loss of 150 jobs.
It became the second bank to announce plans to close last month after ACC Bank said it was to hand back its banking licence next year.
Danske customers with savings accounts will be told to close their accounts two months from the date of the letter from the bank.
Customers have been informed in the letter they can withdraw any balance by electronic transfer. Customers will have to have another account to accept money coming out of the account they are shutting.
The letter states: "If your account includes a debit card you should destroy all Danske Bank debit cards once your account is closed by cutting through the magnetic strip."
Customers have been warned they must operate their account in line with the terms and conditions until the close-down date. People with more than one account, and those with a credit card, will get letters in the coming weeks. Mortgage accounts are unaffected.
Danske said it now plans to focus its business towards corporate and institutional clients.
Existing personal customer products and services will be phased out during the first half of 2014.
The shutdown decision comes after Danske Bank Ireland recorded a loss before tax of €1.4m for the first nine months of 2013.
Danske said existing business customers will still be supported by the bank while mortgages and personal loans will continue in line with existing terms and conditions.