“Three of our citizens lost their lives. One of them is a child, another a teacher,” Suleyman Soylu said on live television, vowing a “strong response”.
Interior Minister Mahmut Ozer said that 10 people had been wounded as a result of the strikes.
The governor of the southeaster Gaziantep province, Davut Gul, earlier said that two people had been killed.
According to the Anadolu official press agency, the strikes hit a high school and two houses as well as a truck near the border crossing that links Karkamis to the Syrian town of Jarablus.
Images on Anadolu showed shattered windows at a school and a truck in flames.
On Sunday, rockets fired from Syria wounded six policemen and two soldiers when they struck a border crossing.
Turkey on Sunday carried out air strikes against the bases of outlawed Kurdish terrorists across northern Syria and Iraq, which it said were being used to launch “terrorist” attacks on Turkish soil.
The overnight raids in northern and northeastern Syria killed at least 31 people, said the British-based monitoring group the Syrian Observatory for Human Rights. They were mainly against positions held by Syrian Kurdish forces.
The offensive, codenamed Operation Claw-Sword, comes a week after a blast in central Istanbul killed six people and wounded 81, an attack Turkey has blamed on the Kurdistan Workers’ Party (PKK).
The PKK has waged a bloody insurgency there for decades and is designated a terror group by Ankara and its Western allies. But it has denied involvement in the Istanbul explosion