The HSE says a formal review is to be carried out into why an emergency ambulance was not made available following a 999 call in Co Cork last Monday.
The call was made after baby Vakaris Martinaitis fell from a second storey window at his home in Midleton, Co Cork.
The baby died in hospital two days later.
The HSE said that a preliminary examination of the case confirmed that an emergency ambulance was immediately available to respond.
The formal review has been called for to establish why it was not made available to the family.
The review team will include experts in pre-hospital emergency care and primary care from both Ireland and the UK.
No date has been set yet for when it is to present its report.
Speaking on RTÉ's Morning Ireland, former Cork hurler Kevin Hennessy said he telephoned for an ambulance after arriving at the scene of the incident.
He was told over the phone that no ambulance was available in the area at that time and he drove injured Vakaris and his father to the SouthDoc service in Midleton.
The child was conscious and crying at the time, he had a graze above his eye and head and also had some signs of swelling, Mr Hennessy said.
Mr Hennessy said he was given a letter at SouthDoc to bring the child to Cork University Hospital.
He then drove Vakaris and his father to CUH.
He said that traffic was heavy en route to the hospital despite it being a bank holiday.
He telephoned gardaí who provided him with an escort.
Tanáiste Eamon Gilmore has said that an investigation into the death of the toddler should be conducted quickly.
He said whatever lessons emerge from the incident should be learned and acted upon.