An air ambulance was among the emergency crews scrambled to Ox Leys Road near Wishaw, off the A38 near Sutton Coldfield, at 7.15pm on Saturday.
West Midlands Police said a number of people were injured and the car driver has since been arrested on suspicion of driving while over the limit and causing injury by dangerous driving.
The car driver, who had minor injuries, remains in custody while inquiries continue.
West Midlands Fire Service used specialist equipment to help six of the seven passengers in the private hire taxi, some of whom suffered serious injuries. A seventh passenger, who suffered minor injuries, was able to get out of the vehicle on their own before crews arrived at the scene.