The blue Ford Focus failed to stop for a police car on Oldfield Lane in New Wortley just before 12pm today.
It then collided with a ride-on lawnmower driven by a Leeds City Council worker before coming to a stop after crashing into the window of Razor's.
A police statement said:-
"The male driver of the lawnmower was taken to Leeds General Infirmary. His injuries are not considered life-threatening. No-one else was injured.
"The 19-year-old driver of the Ford was arrested on suspicion of dangerous driving and possession of drugs with intent to supply. He is currently in custody.
"Road closures are currently in place while the scene is dealt with an the damaged building is assessed.