The incident occurred while Gul Mohammad was taking his daughter to a hospital for a medical check-up, according to an India Today report.
The BMW has been seized and two college students — Yash Sharma and Abhishek Rawat — have been arrested, the Noida Police confirmed.
Gul Mohammad and his brother-in-law Raja, who were on the two-wheeler, are undergoing treatment and remain in critical condition.
Police said an investigation is underway to establish the sequence of events and to determine whether the accused were speeding, driving rashly, or under the influence.
Officials have assured strict legal action against those responsible.