Calm was restored to the streets of central Dublin on Friday night amid a heavy police presence after 34 people were arrested following rioting the previous night that was triggered by the stabbing of three young children in the street.

Police were on alert for further violence after rioters smashed shop windows; set fire to police cars, buses and a tram; and clashed with officers in and around the main thoroughfare of O'Connell Street in violence rarely seen in the Irish capital.

Shoppers and tourists returned on Black Friday morning, passing officers guarding looted stores as burnt out vehicles were removed. Police chased a few people from the street on Friday evening and made some arrests but the city was quiet.

"Those involved brought shame on Dublin, brought shame on Ireland and brought shame on their families and themselves," Irish Prime Minister Leo Varadkar told a news conference early on Friday of the violence overnight.

A five-year-old girl remained in a critical condition on Friday following emergency treatment for serious injuries sustained in the stabbing, which happened near a school and beside O'Connell Street.

Police, who say they have not ruled out any motive including whether it was terror-related, have not commented on the nationality of a man detained in connection with the stabbings but there was immediate speculation online that he was foreign.

The man is in his late 40s and being treated for serious injuries. Police said they were not looking for any other suspect.

Police blamed far-right agitators for starting the violence after a small group of anti-immigrant protesters arrived at the scene of the stabbing and clashed with police. (Reuters)