The crash happened at Bilston Street Island on the city's busy ring road at around 8.20am.
Paramedics and police remained at the scene into this afternoon where the shell of the car remains after firefighters had to cut the roof off to free the female driver inside.
She was taken to hospital with an arm injury and whiplash but is not thought to have been seriously hurt.
Four people from the tram, including the driver, were treated and discharged at the scene.
The tram, which is dedicated to football legend Cyrille Regis and was carrying 29 people at the time, was knocked off the tracks as it crossed the roundabout heading towards the A41 Bilston Road.
It was left with major damage to its front end and to the side of the first carriage.
The crossing between the entrance and exit to the A41 is still closed, as is the section opposite the Novotel, so any cars coming into the island via the A4150 are being diverted down the A454, while the incoming traffic from the A454 is being diverted up the A41.
All other traffic is able to flow but there are delays on surrounding roads and disruption is expected throughout the day until the tram is recovered.
Meanwhile West Midlands Metro trams are terminating at The Royal, with tram tickets being accepted on trains between Birmingham and Wolverhampton and on the number 79 bus for people needing to get between The Royal and Wolverhampton city centre.
Trams were running on an eight-minute schedule but officials warned passengers to expect delays into the evening.
Service update: we are still running between The Royal and Grand Central only due to a road traffic collision earlier. Tram tickets and passes are being accepted on the 79 bus and on west midlands railway between Wolverhampton and Birmingham. pic.twitter.com/OdiQMee7So— West Midlands Metro (@WMmetro) August 19, 2019
A West Midlands Ambulance Service spokesman said: “The driver of the car, a woman, was the only occupant of the vehicle and she had to be cut free through the roof with the help of the fire service.
“She was assessed by ambulance staff and treated for injuries not believed to be serious before being taken to New Cross Hospital in a stable condition.
“There were 29 people on the tram, 25 of whom did not require treatment or assessment.
“The driver, a man, was treated for minor injuries and discharged at the scene.
“Two women, who were passengers, were treated for the effects of shock, whilst a man, also a passenger, was treated for non-serious injuries. Again, all three were discharged at the scene."
British Transport Police is investigating.
A spokesman for West Midlands Fire Service said 15 firefighters from three crews were sent to the scene and stabilised the car before cutting it open.