Gardai said that two suspects entered the bank at approximately 11.40am.
It is understood that one was armed with a sawn-off shotgun and that a sum of money was taken during the incident.
The raiders are understood to have hijacked a taxi in the Dublin 8 area prior to the bank robbery.
They then used this vehicle to escape.
A garda helicopter was deployed immediately and gardai were on the scene within minutes.
A source revealed how the raiders only managed to evade garda road blocks by a matter of ‘mere seconds.’
Witnesses in nearby buildings spotted several men running around the top of the copper roof of the iconic building in Dublin's city centre just after midday today.
Staff at the bank were said to be extremely traumatised by the incident. A representative for Bank of Ireland said that that the bank would not comment on security matters.
The incident follows a number of raids on financial institutions in the capital in the last week alone. Last Friday, a bank and a credit union in North Dublin were raided. In the first incident, two armed men entered a Permanent TSB in Phibsboro at around 4:15pm.
They fled with a small amount of cash but were detained just minutes later by gardai.