Emergency services were called to Bramley Lane, Woolley, at 10.20am this morning.
The black Honda Civic had left the road and hit a wall and then a tree.
Pictures from the scene show the car overturned with major damage.
A spokesperson for West Yorkshire Police has confirmed the driver and a passenger suffered minor injuries in the crash.
One man was taken to hospital as a precaution.
The road has now reopened.
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