The incident occurred on the Link Road near Amboliin the Andheri West suburb around 6.30 a.m. The other car was thrown off the road and overturned.
The 42-year-old actor was driving his Mercedes at a high speed when he rammed into the oncoming car in which a family was travelling.
The victims have been identified as Deepak Darera, 60, his wife Kanta, 55, and their daughters Pooja, 24, and Sneha, 28, police said.
Three of the four members of the Darera family from Lokhandwala Complex in Andheri were injured. One of them is reported to be critical at the Kokilaben Ambani Hospital.
Following a complaint by the victims, Roy was arrested and presented before a holiday magistrate in Bandra.
Charged under Indian Penal Code Section 279 (rash driving) and 338 (causing grievous injury endangering lives), Roy was released on bail of Rs.12,000 in the afternoon.
Police are awaiting his medical report to ascertain whether he was drunk at the time of the accident.
While Sneha escaped with negligible bruises, Pooja received a few cuts on her head which had to be stitched, while their father sustained hand injuries. Kanta Darera suffered severe injuries on the back and is undergoing treatment.
At the time of the incident, Roy was returning from a Diwali party and the Darera family was on way to spend the weekend at the Matheran hill station in adjacent Raigad district, police said.
Moments after the accident, Roy got out of his car and helped the victims by taking them to hospital in a cab, and left without informing police.
The police acted only after the victims complained and arrested Roy.
Pooja told mediapersons outside the police station that Roy was zooming at over 100 kmph speed and hit their vehicle.
The usually crowded Link Road, one of the main thoroughfares linking north-south suburbs from Borivli to Bandra in the city, was almost deserted on account of the festival holidays at the time of the incident.
The actor started his career with the movie “Jaan Tere Naam” in 1992 and later featured in “Kisna”. Last year, he acted in film “Udaan”.
He earned popularity on television with shows like “Kyunki Saas Bhi Kabhi Bahu Thi”, “Kasautii Zindagi Kay” and “Bandini”. Currently he stars as a successful lawyer in the weekly show “Adaalat”.