Eamon Gilmore and Frances Fitzgerald arrived at the Base, a youth centre in Ballyfermot, to promote the children’s referendum but abandoned the event when their car was attacked by protesters.
Supporters of republican group Éirígí and People Before Profit surrounded the car, which was egged, kicked, and rocked.
A 28-year-old man was arrested and later charged in relation to the incident.
Mr Shatter condemned the violence and thuggery shown by protesters and their callous disregard for children.
“Such thuggery and violence cannot and will not be tolerated in a free society,” he said.
Mr Shatter said the ministers withdrew because of the violent and threatening behaviour of the protesters and because of concerns for the safety of children attending the event.
He said he had been assured by the gardaí that they would pursue fully any illegal behaviour that occurred.
Ms Fitzgerald said it was a very aggressive protest.
“There was a lot of punching of the car, banging on the roof of the car, banging on the windows, a lot of obscenities shouted. I was concerned. We had a 100 children waiting for us to go in.”
The protesters included Éirígí councillor Louise Minihan, who stood back from the ministerial car and was not involved in the attack.
Ms Minihan, a member of Dublin City Council, was imprisoned for seven days earlier this year for not paying a €1,500 fine for throwing paint on former health minister Mary Harney.
Local Fine Gael TD Catherine Byrne said she would be writing to the city manager requesting Ms Minihan’s dismissal from the council.
Ms Byrne said Ms Minihan was appointed to the city council as a member of the board of the Base.
“I believe she has abused her position by being involved in the ugly protest,” said Ms Byrne.
Labour TD Michael Conaghan said the protesters who had tried to spoil the young people’s celebration did not represent Ballyfermot.
“They should be ashamed of themselves,” he said.
Peter Power, Unicef executive director, said the event had been organised to bring young people right into the heart of the referendum campaign.
Unicef’s campaign — It’s About You — includes a video explaining the referendum and a resource pack for thousands of schools and youth groups throughout the country.
Mr Power said children at the event emphasised the importance of free speech: “So it is ironic that some people did not get the opportunity to express themselves freely.”
A number of children were invited to join Ms Fitzgerald and Mr Gilmore for the launch of the campaign at the Department of Foreign affairs in Iveagh House later in the day.