Senior executives from Ulster Bank will be asked to appear before an Oireachtas committee to answer questions about today's IT problem, which the bank has blamed on "human error".
Hundreds of complaints were posted on social media this morning, with some people claiming that their salaries have disappeared.
Some customers said they have had their cards declined when making purchases, while others have said they have direct debits due and insufficient funds in their accounts to cover them.
The Joint Committee on Finance and Public Expenditure agreed this afternoon to invite Ulster Bank to Leinster House.
It follows a request from Sinn Féin TD Pearse Doherty to the committee.
The Minister for Finance said the Central Bank is reviewing issues at the bank after some customers claimed money has gone missing from their accounts.
Paschal Donohoe said it is a concerning development and a real worry for any customers caught up in the IT problem.
In a statement, Ulster Bank said it was aware that transactions applied to accounts since last Friday are no longer showing.
We are aware that some transactions previously applied to accounts for ROI customers since 20/04 are no longer showing. We are working hard to fix this issue and apologise for any inconvenience. https://t.co/25K9Vm8L8H— Ulster Bank Help (@UlsterBank_Help) April 24, 2018
The lender said: "As a result of human error, a payment file did not process last night, which means that some transactions applied to some customers accounts since 20 April are temporarily not showing.
"We investigated this issue as a matter of urgency and have already taken the necessary corrective action which will see recovery actions overnight."
The statement added that emergency cash of up to €500 is available in branch or over the phone, with the correct identification.
The bank said it was working to have affected transactions processed overnight tonight and return customers to their normal position.
It said no customer would be left out of pocket and that not all customers were affected by the issue.
The Central Bank said it is aware of "an issue involving the bank accounts of certain Ulster Bank customers" and that it is monitoring the situation "and is in contact with the firm in relation to this matter".
The regulator added that it expects "all firms to have adequate systems and controls in place and where issues that impact customers arise they should be addressed and rectified urgently, particularly as customers are increasingly using and becoming dependent on online and mobile banking services".
Ulster Bank suffered a huge system crash in 2012 that deprived customers of basic banking services for almost a month.
The IT glitch cost the bank €59m in compensation and a €3.5m fine from the Central Bank.
When asked what kind of fine could be imposed in this instance, Mr Donohoe said it was a matter for the Central Bank.
Additional reporting: Conor Hunt