Police said the victims, both women, were standing near the steps on the first floor when the balcony of the second floor of the Slum Clearance Board building caved in on them around 11.30 PM last night.
One of the women died en route to the government hospital, while the other was later admitted to a private hospital.
Inmates of more than 100 houses in the Slum Clearance Board building staged a blockade demanding compensation for the victims.
On June 28, 61 persons were killed when an under construction multi-storeyed private building collapsed near Chennai.