A five-year-old Irish boy suffered a broken leg when his family was caught up in the terror attack in Barcelona.
The boy's father also has leg injuries after a van was driven into innocent people in Las Ramblas, one of the busiest avenues in the Spanish city.
Ireland's Foreign Affairs Minister, Simon Coveney, said: "They are not life-threatening, I'm relieved to say.
"But in a way it's a miracle that more Irish people weren't involved, given that there are so many Irish people in Spain, Barcelona and Cambrils at this time of year."
The father and son were part a family of four, including the mother and a daughter, and are understood to have been on a trip to celebrate the boy's birthday.
The youngster suffered a broken femur.
The mother and father are understood to be from Cebu in the Philippines and are naturalised Irish citizens. They hold dual citizenship. The children were born in Ireland.
Ireland's Department of Foreign Affairs is assisting the family.
Its officials opened a hotline in Dublin for anyone concerned about relatives in Spain on 01-408 2000 while the Irish Embassy in Madrid was also fielding calls on +34 9143 64093.
President Michael D Higgins led condemnation of the attacks and sent a message of condolence.
"Barcelona has a long history of hospitality and has over the years received so many people from around the world," he said.
"As President of Ireland, I want to send the people of this great and welcoming city not only our sympathy but also the solidarity of the people of Ireland."
Taoiseach Leo Varadkar said: "An attack of this nature, targeting the people of Barcelona and visitors enjoying that wonderful city in the height of the tourist season, is both wanton and cowardly and has no place in our society.
"At this time of immense grief, I want to offer our solidarity and support to the people of Spain, with whom we have such close relations."
Mr Coveney said he was appalled by the attacks.
"On behalf of the Irish Government, I wish to convey our condolences and solidarity with the people of Spain at this time," he said.
Justice Minister Charlie Flanagan described it as an unspeakable act of terrorism and vowed that gardai would liaise closely with Spanish counterparts.
"It is clear that the intention of those who carried out this appalling, evil act was to kill, wound and terrorise innocent people enjoying the freedoms we share and cherish," he said.
"Our thoughts are with the victims and their families."