The incident occurred on Thursday, December 7, near the New Ireland Road, Rialto.
Officers from Kilmainham Garda Station are investigating the incident and have appealed for witnesses to contact them.
A source last night told the Herald: "Gardai are carrying out a detailed investigation into this incident, and the possibility that there is an organised crime element.
"It is a very large amount for someone to have on their person," the source added.
Gardai are reviewing CCTV footage from the area around the robbery.
The victims, in their 30s and 50s, withdrew cash from a bank on the Crumlin Road on the day of the theft. They then drove toward the Rialto area and parked the car at around 12.45pm.
As the passenger left the car, a lone man on foot - who was described as 5ft 9in - approached the victim and pushed her back into the car.
A handgun was produced and the man made off with a handbag containing the €55,000 and the car keys. The suspect, wearing dark clothing, a hi-vis vest, sunglasses and a helmet, fled on a bicycle down New Ireland Road.
"Gardai are appealing for witnesses or anyone with information to contact them - in particular about anyone they may have seen acting suspiciously around South Circular Road or New Ireland Road prior to the robbery," a spokesman said.
"Gardai are also seeking motorists who were travelling from St James's Hospital to Rialto on South Circular Road, Dublin, who may have a dash camera," he added.
The times of particular interest are between 12.30pm and 1pm on December 7.
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