The bank said that its decision to exit the market here, where it has been based since 1997, was an attempt to boost its balance sheet.
MBNA is one of the largest credit card providers in Europe, employing some 4,000 people with $19bn (€13bn) in credit card loans.
But the majority of staff only got an indication that there was something wrong when relatives called them yesterday, having heard media reports in the US about the company's plans.
Managers were summoned to a meeting later that afternoon and according to staff, e-mails were received by workers at around 3pm but there was no meeting called.
Jobs, Enterprise and Innovation Minister Richard Bruton said he had contacted Bank of America officials after the announcement.
"I have also spoken to the IDA and asked them to work closely with the company with a view to assisting them finding a buyer for the business as a going concern," he said.
Bank of America is mired in lawsuits challenging its settlement to mortgage securities investors after its ill-fated acquisition of home mortgage lender Countrywide Financial.
The group lost more than $22bn (¤15bn) in its consumer mortgage division for the past four consecutive quarters.
"While the credit card remains a fundamental core product for our US customers, an international consumer card business under another brand is not consistent with our strategy," said Bank of America CEO Brian Moynihan.
The US bank also announced plans to sell its Canadian credit card business.
The group outlined that the credit card sector was no longer part of the core sector of its business and the bank now had a "stated desire" to exit its Irish and UK MBNA business.
As it was not branded Bank of America, the business had "little connection" to the rest of what the bank could offer.
However a spokesman confirmed that the business was "a strong business".
"We announced our intention to exit the business because it is not core to our strategy," he said.
"The customers that came to us for this service were strictly card customers. They had no other relationship with the bank and they don't fit into the core strategy that we are trying to emphasise to grow our business around the world."