The infant died after the incident involving a car at a halting site in Ennis, Co Clare, early on Wednesday afternoon.
The child was rushed to University Hospital Limerick at about 12.30pm, but was later pronounced dead.
It has emerged that the boy’s mother, who has two other children, is due to give birth next month.
Gardaí were at the scene of the incident yesterday evening as they tried to piece together what had happened.
Their investigation will include forensic examinations of the scene and a car.
Ennis parish priest Father Tom Ryan visited the Ballaghboy halting site on the Quin Road in the town, where he offered his sympathies to the boy’s parents and members of their extended family.
Yesterday evening, Fr Ryan met and said prayers with the child’s parents and the wider family.
Fr Ryan had christened the child, along with his siblings, and also married the children’s parents.
Fr Ryan said the boy was due to celebrate his second birthday in October.
“This is just a pure tragedy to beset a family – a tragedy of the worst kind,” Fr Ryan said.
“I visited the family this evening and we gathered for a little prayer service on the grounds of the site.
“Praying for each one of them that they would have the strength they need at this time to be able to cope with the devastating news bestowed on them today on the death of this little child in the tragic accident.
“The sympathy and the prayers of the community are with them.”
He said the visit to the site to be with the family was “a necessary one” to make.
“It is not just a family but families, as they are all extended families who are plunged into sadness and tragedy by one second,” the priest said.
“They need support and as a parish priest I was offering them that support, and I would have known the family for many years.
“I was privileged to marry the parents a numbers of years ago. They are just devastated and trying to come to terms with this news.”
Fr Ryan said the boy had two sisters and their mother was expecting another child next month.
Gardaí said a family liaison officer had been appointed to support them.
The boy’s death brings to 72 the number of road fatalities nationwide so far this year.
The number of deaths is outpacing the number of those who died last year. Overall, 184 people died on roads last year, according to the Road Safety Authority.
Last year’s total was an increase of 19pc in road fatalities compared with 2022.