Royal Mail's computer system which deals with benefit payments has broken down.
The problem has affected the benefits system
It means anyone with a Post Office Card Account cannot withdraw money. It is not known how many customers in Northern have been affected.
Royal Mail said urgent talks were under way to try to get the system fixed.
Emergency payments of £20 will be made to those most in need, but the Citizens Advice Bureau said the problem needed to be urgently addressed.
The computer system, known as Horizon, stopped working on Tuesday and post offices across the UK are affected.
About 600,000 people get money from benefits system, however, Royal Mail have been unable to say how many of those have card accounts.
Derek Alcorn, chief executive of the Citizen's Advice Bureau in Northern Ireland said anyone who needed help should visit one of their offices.
"These are socially vulnerable people and they're relying on benefits and any drop in their income at all, if you're on the breadline, will affect people," he said.
"It will affect people in terms of what they can eat, whether they can heat their house, whether they can get transport.
"So it's quite urgent really that this is sorted out very quickly."
The Post Office Card Account can only be used to receive benefit, state pensions and tax credit payments.
It allows a person to take cash out, free of charge, at any Post Office branch using a plastic card and Personal Identification Number (PIN).