The incident occurred when a speeding car rammed into the two two-wheelers, which the four deceased were riding, on the causeway connecting Panaji to Ribandar area, a police official at Old Goa police station said.
The deceased have been identified as Dattaram Parab (43), her daughter Angel (7), Olga and Ankit Gandhi, who belonged to Nagpur.
Parab was travelling with her daughter Angel and Olga on a bike, while Gandhi, was on a scooter when their vehicles were dashed from behind by the speeding car.
The car also fell into the river and it's occupants were saved by people near the banks who pulled them out, police said.
The four victims were taken to Goa Medical College and Hospital where they were declared brought dead, police added.