News agency PTI reported that the accident took place near Ismailpur village, about 25 kilometers from Ambala city.
The body of the Punjabi family was later fished out of the Narwana branch canal.
Police said the deceased have been identified as Kuldeep Singh (48), his wife Kulbir Kaur (40), son Sukhpreet (15) and daughter Jashndeep Kaur (10).
Police said Kuldeep Singh hailed from Tiwana village (near Lalru) in Punjab and was on his way to Ambala along with his family members in his car, as reported by news agency PTI.
The case is under further investigation.