The accident occurred in the Meriç district of the province when the driver reportedly lost control of the vehicle and crashed into a wall.
"A number of migrants were injured and hospitalized after the incident," the Demirören News Agency reported.
Ekrem Canalp, governor of Edirne province, went to the crash scene for inspection.
Edirne, bordering both Greece and Bulgaria, has seen an influx of migrants seeking to cross into the European Union.
Turkey has been a key transit point for irregular migrants aiming to cross into Europe to start new lives, especially those fleeing war and persecution.