Barricades were up across some shopping streets where Black Friday sales were due to take place. Police stood guard outside a Foot Locker store with broken windows that was looted during the riot. The front of a Holiday Inn hotel was boarded up.
A five-year-old girl was receiving emergency treatment after sustaining serious injuries in the stabbing.
Harris said the girl remained in a very serious condition with a female teacher in her 30s also in a serious condition.
The two other children, a five-year-old boy and six-year-old girl, suffered less serious injuries.
The detained man in his late 40s, also being treated for serious injuries, was detained by police who said they were not looking for any other suspect.
Harris said police had not ruled out any motive, including whether it could be terror-related.
There are no far-right parties or politicians elected to Ireland’s parliament, but small anti-immigrant protests have grown in the last year.
The government is reviewing security around parliament after a recent protest trapped lawmakers inside.