Gardai are treating their deaths as a family tragedy.
At around 3:45 this morning, Gardai received reports of a pedestrian acting suspiciously at the M50 Toll Plaza bridge.
When they responded to the reports, they found the body of a woman at Lower Road in the Strawberry Beds area.
Officers then went to a house in nearby Lucan where a 7 month old boy was found in an unresponsive condition.
The baby was pronounced dead at the scene a short time later.
The boy's body has been removed to Crumlin Hospital and his mother's body to the City Morgue for post-mortem examinations.
Gardai are treating their deaths as a family tragedy and aren't looking for anyone else as part of the investigation.
The family of the mother and child have appealed for privacy.