The incident took place around 10 pm when Bajpai was returning to his home in Mohanpuri locality here after attending a party function, BJP state secretary Ashwani Tyagi told PTI.
The car overturned after the driver lost control over it and the vehicle hit a divider, SHO, Civil lines, Iqbal Ahmed said, adding, Bajpai was rushed to a nearby hospital where his condition was stated to be stable.
One of his office-bearers was also injured in the incident, the SHO added.