The 3.5 million euro (USD 4.4 million) fine is the largest ever handed out by the central bank and was the maximum it could impose.
"The Firm failed to have robust governance arrangements in relation to its IT systems and controls and... As a result, a major and prolonged IT failure occurred," the Central Bank of Ireland said in a statement.
As well as causing "widespread and significant loss and inconvenience" to customers, the meltdown also "threatened confidence in the operation of the retail banking sector" as it prevented payments clearing, it added.
Owned by the British state-controlled Royal Bank of Scotland, Ulster Bank has since paid 59 million euros to affected customers in compensation.
"Our customers need to be able to rely on our systems and in this instance we let them down," Ulster Bank chief executive Jim Brown said in a statement, saying the bank had taken steps to ensure such a failure could not recur.