The woman was flown from the scene by air ambulance to a Dublin hospital for treatment for serious injuries
Gardaí in Mullingar are investigating “all the circumstances” surrounding the deaths, a spokesman has said.
A woman is also in hospital with serious injuries sustained in the blaze which occurred close to Multyfarnham, Co Westmeath.
Shortly before 4pm, the alarm was raised after a car with three occupants was discovered on fire on a rural road at Lackan near Multyfarnham.
An infant boy was removed from the scene by ambulance to Midland Regional Hospital, Mullingar where he was pronounced dead.
The remains of a juvenile female were also discovered inside the car at the scene. Her remains have been removed from the scene to Midland Regional Hospital, Tullamore.
A woman was treated at the scene for burn injuries. She was taken by air ambulance to a Dublin Hospital. Gardaí said her injuries are understood to be serious but not thought to be life threatening.
The scene has been examined tonight by the Garda Technical Bureau and remains preserved overnight. The car has been removed from the scene and will be further forensically examined tomorrow.
The scene has also been examined by the State Pathologist, Dr. Sally Ann Collis. Dr. Collis will carry out post mortems on both deceased in the Midland Regional Hospital, Tullamore tomorrow. The Coroner has been notified.
The results of the Post Mortems and the Forensic examinations will determine the course of the investigation.
An incident room has been established at Mullingar Garda Station and Senior Investigating Officer (SIO) has been appointed to lead the investigation.
A Garda family liaison officer has been appointed and An Garda Síochána will continue to support the family involved in conjunction with other state agencies.
An Garda Síochána is appealing to any person with any information in relation to this fatal incident to contact investigating Gardaí at Mullingar at 044 9384000, the Garda Confidential Line 1800 666 11 or any Garda Station.
Gardaí at Mullingar are investigating all of the circumstances surrounding the deaths.
Sinn Féin TD for Westmeath-Longford, Sorca Clarke, described the incident as “desperately sad”.
“Desperately sad news from Multyfarnham. Thoughts and deepest sympathies with the family, friends and loved ones. Thoughts also with the emergency services and all who came to their aid,” Deputy Clarke said.
Brian Crum, Fianna Fáil representative for Multyfarnham, said the thoughts and “heartfelt sympathies” of everyone in the area are with the family involved.
“You hear of tragedies like this happening in other countries or in other counties, but you never expect something like this to happen where you’re from, or know what it feels like until it comes from your own area - especially when you have children of your own. Multyfarnham is a very tight knit community, everyone sticks together and helps each other out. This tragedy will be felt right across the community, “Mr Crum told Independent.ie.