The incident took place yesterday night and the police initially received information about a road rage incident in the area.
The bike rider was arrested on the charge of rash driving and the one and a half-year-old child, Manan, and his father, Ashok, were taken to a hospital where the boy died during treatment, a senior official said.
During investigation, it emerged that Ashok was driving the auto-rickshaw and Manan was seated next to him. By the impact of the collision, Manan fell on the road and received injuries on his head.
Ashok has been shifted to another hospital where he underwent surgery on his limbs.