Four of the victims were identified as Munira Shaikh, 25, Rajul Moinuddin Shaikh, 4, Alisha Shaikh, 40, and Rashida Shaikh, 20.
They were admitted to Sir J.J. Hospital with multiple fractures and other injuries, police said.
After the accident, the driver, Haji Amin Khan, fled the scene near Masjid Bunder in south Mumbai. But he was arrested around daybreak.
Khan was taken for a medical test to ascertain if he was inebriated. A magistrate later granted him bail.