Danske Bank is expected to axe up to 150 jobs as it pulls all but its corporate services out of the Irish market.
The finance house has announced that its day-to-day personal and business products and services will be withdrawn on a phased basis during the first six months of next year.
But the bank, formerly National Irish Bank, said it will remain committed to its corporate and institutional clients.
A spokeswoman for Danske said talks had started with the banking unions as it was "anticipated" 150 jobs could go,
It is the second institution to quit the Irish market in a week, after ACC Bank announced plans to close all its branches and business centres with the loss of about 180 jobs.
IBOA general secretary Larry Broderick said it was a sad day for staff and consumers.
"We are in shock," he said. "We always argued the decision to close the retail branch network two years ago was wrong."
Danske Bank previously closed 27 branches and re-opened seven advisory centres, with the loss of 100 jobs.
Its latest cuts were revealed as figures showed a loss before tax of 31.4 million euros for the first nine months of 2013, while it also recorded impairment charges of 22.8 million euros.
Gerry Mallon, head of Danske Bank UK & Ireland, said: "The decision regarding the personal and business banking divisions is necessary to stem the losses that continue to accrue in those units.
"Against the backdrop of the difficult economic and trading environment in Ireland, the bank has been unable to re-establish a sustainable retail banking business model.
"We appreciate that this announcement will be of concern to our personal and business customers."
He added that there will be no changes for existing personal customers until the first half of next year.
Mortgages and personal loans will continue in line with existing terms and conditions.
Customer deposits will be repaid in full and continue to be covered, through combined protection under the Danish Guarantee Fund for Depositors and Investors and the Irish Deposit Guarantee Scheme, up to a maximum of 100,000 euros per depositor.
"We are writing to customers in the coming weeks and will be working with them to minimise the impact on their day-to-day banking needs," he said.
"We acknowledge also the impact this will have on our staff. We will be working closely with them through this process and commencing the appropriate consultation immediately."
Mr Broderick said he was told last night about the announcement, which was made this morning in Copenhagen as Danske Bank Group published its quarterly results.
"This announcement is particularly traumatic for Danske Bank workers in the Republic of Ireland as it is likely to result in compulsory redundancy for many," he said.
"We have urged Danske Bank Group to reconsider this decision in the interests of its Irish customers as well as its staff.
"It is disappointing that Danske Bank is moving to withdraw still further, to the obvious detriment of its customers and its staff."
The IBOA said it will enter discussions with the bank at the earliest opportunity in an effort to ensure that any redundancies are implemented on a voluntary basis.
"We will also focus on the terms of the redundancy compensation in view of the huge impact of the closure on our members," Mr Broderick said.
"We will also urge the Irish Government today to ask Danske Bank to reconsider its position in the interests of its customers and staff in the Republic of Ireland."
Irish Farmers' Association president John Bryan said Danske's shutdown puts an onus on the Government to keep the remaining banks honest.
"Following on from the announcement by ACC last week, this move by Danske reduces further the options open to farmers, small and medium enterprises and consumers who need competitive banking facilities to run their businesses," he said.
"The Government and Financial Regulator have a responsibility to increase the oversight of the banks remaining in the market and, if necessary, introduce price controls on the interest and credit charges they impose on their customers so they do not exploit this situation by increasing the cost of loans and banking facilities."