The boy had been with his siblings and mother, who had an appointment at the welfare office on the building's first floor.
The three-year-old was the only person injured at the office block on St Augustine Street.
The boy's mother is originally from Nigeria but had been living in the city for a few years.
Gardai, the Health and Safety Authority (HSA) and building management are to carry out investigations.
The Hynes Building has been closed and inspectors from the HSA and gardai have been examining the scene.
The three-storey block houses a number of offices, including some of the city's Department of Social Protection divisions and staff, and the regional office of the national broadcaster RTE.