In a statement the bank said it apologised for the error.
It added that it had investigated the issue as a matter of urgency and took the necessary corrective action which saw recovery actions overnight.
Ulster Bank has said this morning that it is aware that money is not showing in some customers' accounts. The bank has stated "No customer will be left out of pocket as a result of this issue".
"What's going on with your banking system again?" Card payments done now missing.
One Twitter user said over €10,000 is missing from his account. Some people have reported that their cards have been declined, while other have said that lodgments are not showing up. I am getting no answer on the phone, every penny gone from both accounts.
"Standing orders/ direct debits due to hit".
At the end of March Ulster Bank also reported delays in payments being processed.
In 2012 a major technical glitch left large numbers of Ulster Bank customers in the Republic with no access to their money for weeks.
Ulster Bank representatives will be asked to appear before the Oireachtas Finance Committee to address the issue.
He called for the Central Bank to "conduct a comprehensive review of the IT systems used by retail banks in Ireland".
Finance Minister Paschal Donohoe yesterday said it was "a very concerning development for any customer of any bank in the state to be anxious about where their money has gone".
"The first some have heard about this is a text message from Ulster Bank telling them they are overdrawn".