According to the police, the family was en route to Nainital when the accident occurred on Friday night.
The deceased were identified as Mukesh Jain (40), Monu (13) and Nishan Singh (34), the police said.
According to police, Singh was driving the vehicle, which the family of Mukesh Jain and his in-laws had hired to travel to Nainital.
Ten others injured were identified as Mukesh's wife Poonam (36), his 22-year-old daughter Khushboo, 14-year-old son Lavish, his mother-in-law Premvati Jain (63), his brother-in-law Sudharshan Jain (44), Sudharshan's wife Kumud Jain (38), their daughter (15) and son Arpit (10).
Two others injured, identified as Priyanka (21) and Anurag (16), were cousins of Sudharshan.
Mukesh hails from Haryana's Gannaur area. While, Mukesh's in-laws belong to Delhi's Uttam Nagar.
According to the police, Mukesh was an accountant with a firm in Mandi House while Sudharshan was a property dealer.
The reason of the accident is not yet clear, but the driver of the water tanker arrested by the Delhi police claimed that his vehicle's clutch was not working properly and the tanker was moving slowly.
"The driver of the water tanker has been arrested and is identified as Santosh Yadav (34). During the interrogation, he revealed that due to faulty clutch the water tanker was moving slowly and it was hit by the mini bus from behind," said DCP (East) Jasmeet Singh.
Further investigation is underway.
( With inputs from IANS )