Protesters on Thursday fought running battles with police, torched vehicles and looted shops in Dublin, after three young children were injured in a knife attack outside a school.

Police in riot gear stood guard on the streets in the Irish capital as crowds taunted them with chants and set off fireworks.

Near O'Connell Bridge, over the River Liffey, flames rose from a torched car and bus, while crowds broke into stores and looted goods on one of the city's main shopping streets.

The unrest – the worst in Dublin in years – came after a five-year-old girl sustained serious injuries in a suspected stabbing in Parnell Square East, north central Dublin.

Two other children and two adults – a woman and the suspected perpetrator of the attack – were taken to hospital after the incident shortly after 1:30 pm (1330 GMT).

Police chief Drew Harris blamed the unrest on a "complete lunatic faction driven by far-right ideology."

He warned against "misinformation" as rumours spread on social media about the suspected attacker's nationality.

One protester said that "Irish people are being attacked by these scum."

Ireland has been facing a chronic housing crisis, with the government estimating that there is a deficit of hundreds of thousands of homes for the general population.

But widespread dissatisfaction has fed into a backlash against asylum seekers and refugees, and far-right figures have promoted anti-immigration sentiment at rallies and on social media with claims that "Ireland is full."

Justice Minister Helen McEntee said the scenes in the city centre, including attacks on police, "cannot and will not be tolerated" and promised to take action.

Thursday's incident, which police said was not thought to be terror-related, involved a man armed with a knife stabbing victims outside the school, according to media and eyewitnesses.

Witnesses told how a man had been disarmed and prime minister Leo Varadkar said a suspect had been arrested. (AFP)