The Volvo sedan, driven by a 27-year-old man, knocked aver a stroller carrying two infants and a five-year-old boy, Zurich cantonal police said.
The man was driving toward the centre of Oberglatt at around 7pm on Sunday when it ran in to the pedestrians, police said.
Investigators are seeking witnesses to find out exactly what happened.
Police did not release details about who was with the children, treated by paramedics before being rushed to hospital.
The conditions of the children were not disclosed.
Officers sought a blood test from the driver.
The accident forced the closure of a section of the Bahnhofstrasse in Oberglatt for three hours.
Anyone with possible information about the collision is asked to contact police on 044 863 41 00.