Police chased a migrant-carrying car at high speed for 150 kilometres after it crossed from Turkey into Greece.
The pursuit finally ended in Thessaloniki when the vehicle jumped a series of red lights and crashed into a passing car.
The smash left 13 people injured, police said. Ten men from Bangladesh — some of whom had been hidden in the boot of the vehicle — and two from Syria were taken to hospital, as was the Greek driver of the other car.
Police began pursuing the car after it failed to stop in Kavala, a northern Greek town 150 km from the Turkish border.
Thousands of people continue to enter Greece from Turkey, either from the coast to nearby Greek islands or through the land border in far northeastern Greece, despite European efforts to stop migrant flows.