Officers were shocked to discover the three-year-old child in the car after the pursuit, which began on Chapeltown Road and ended on the A643 in Holbeck, close to junction 2 of the M621, on Wednesday.
The driver failed to stop for police crashing into two cars. He was caught and detained soon after fleeing the vehicle.
The child and the occupants of the two other vehicles were unhurt.
The 32-year-old man is in custody on suspicion of multiple offences.
A driver who crashed a car while fleeing from police then abandoned a four-year-old child in the back seat.
West Yorkshire Police had been pursuing the Ford Fiesta ST in the centre of Leeds on Wednesday afternoon.