The incident occurred last evening at Ading village when the woman (Kamla), her daughter (Kavita) and her husband Hari Singh were returning after pilgrimage at Goverdhan hillock.
Superintendent of Police Aditya Kumar Shukla said the speeding car fell into the canal after a suspected collision with some object.
Soon some villagers and passersby reached the spot and fished out the woman and her daughter, while her husband himself swam to safety, the SP said.
The family from Palwal in Haryana was returning after performing a circumambulation of the Goverdhan hillock, Shukla said, adding the bodies have been sent for post-mortem.