Police were called to the scene in Jobstown, Dublin, and they deployed a helicopter and their public order unit.
The protesters targeted Deputy Prime Minister (Tánaiste) Joan Burton as she was leaving a graduation ceremony.
Officers got her out of the car and transferred her into an unmarked police car, which was able to leave the scene.
State broadcaster RTÉ reported police officers had earlier tried to free her car by pushing it forward "inch by inch".
It said that about 100 protesters were involved in the incident and that eggs were thrown during scuffles.
The protesters chanted "we won't pay" and some chased after the minister as she was driven away in the unmarked police car.
The Irish coalition government has recently faced unprecedented protests over its recent introduction of domestic water charges.
The charges are being imposed in every household in the Republic of Ireland and the bills will begin to arrive early next year.
The new measure was a condition of the international deal struck in 2010, when the state sought a multi-million euros bailout from the International Monetary Fund (IMF) and European Union.
Earlier this week, anti-water charges protesters disrupted the Irish government's official announcement of its plans for the 1916 Easter Rising centenary commemorations.
The protesters gathered outside the event at Dublin's General Post Office - the focal point of the original 1916 rebellion - and staged a noisy demonstration.
They banged loudly on the doors and windows, drowning out speeches by Ms Burton and Irish Prime Minister (Taoiseach) Enda Kenny.
One man was removed from the event when he heckled Mr Kenny from the audience.
On 1 November, tens of thousands of people took part in nationwide marches against the introduction of water charges.
Anti-water charges protesters have surrounded the Irish deputy prime minister's car, trapping her vehicle which was unable to move for two hours.