The two officers were released Wednesday pending the conclusion of the investigation after appearing before an investigating judge in the northeastern town of Orestiada, near Greece's land border with Turkey.
The frontier is a major illegal entry point for migrants seeking a better life in Europe, lately with the encouragement of Turkish authorities, which earlier this year threw open their borders with Greece to asylum-seekers and berated Athens for not letting them in.
A police statement said the two migrants — a man and a woman who had been shut in the trunk of the car — suffered flesh wounds from bullet fragments and were discharged from a hospital after receiving first aid.
The statement said the incident occurred Saturday near the border village of Mikro Dereio, when a car driven by a 36-year-old Syrian man ignored police orders to stop. Police said the driver tried to ram the police car during the ensuing chase, after which the two officers fired warning shots in the air and then, when the car still didn't stop, at its tires.
The people in the car were all Syrian and Somali nationals. They are believed to have paid a human trafficking gang to smuggle them across the border from Turkey and to take them to the northern city of Thessaloniki.
The car's driver was arrested. The migrants were taken to a center for asylum-seekers pending examination of their applications to be granted refugee status. To cut down on costs, smugglers routinely cram large numbers of migrants into cars, and use country roads in the hope of avoiding police roadblocks. Crashes are frequent.