Two of those hurt were badly injured, Huseyin Sanverdi, the mayor of Reyhanli, a small town situated in Hatay province on the Syrian border, told NTV television. Earlier, several rockets hit the Turkish border town of Kilis without causing fatalities.
The Dogan news agency said that three rockets had hit the centre of Reyhanli, damaging buildings and parked vehicles.
Turkish forces on Saturday began a major new operation aimed at ousting the Peoples' Protection Units (YPG) Kurdish militia from Afrin, pounding dozens of targets from the sky in air raids and with artillery.
Turkey accuses the YPG of being the Syrian offshoot of the Kurdistan Workers' Party (PKK) which has waged a rebellion in the Turkish southeast for more than three decades and is regarded as a terror group by Ankara and its Western allies.
Foreign Minister Mevlut Cavusoglu said on Twitter that this "terrorist attack" against civilians in Reyhanli had shown the "true face" of the YPG.