Mashun Ertugrul, 17, was walking on the street when he was hit by the chest and was taken to the hospital, where he died, Today's Zaman said.
Ahmet Gunduz, 16, was hit in the head while watching TV indoors. He is in critical condition, Today's Zaman said.
The stray bullets were fired at about 11:30 p.m. Tuesday, during clashes between the Free Syrian Army and the Democratic Union party, the Dogan News Agency said.
The stray bullets sporadically target or accidentally hit Turkey's southern bordering towns near Syria.
In 2012, a mortar shell fired from Syria landed in a Turkish residential district and killed five people.