The accident took place when the car hit a divider after colliding with the animal, SP (Rural) Aditya Shukla said.
The deceased have been identified as Shobhit (35), Kanhaiya (12), Roshani (10), Santosh Singh (34).
According to the police, all the injured have been admitted to a private hospital and their condition is stated to be stable.
All the people were returning to Ferozabad after attending a family function in Delhi, the police said, adding the bodies have been sent for post-mortem.