The militant had fired from Syria's Ras al-Ayn region into Turkey's Sanliurfa province, the source said.
Turkey considers the YPG militia a terrorist organisation and an extension of the outlawed Kurdistan Workers' Party (PKK), which has waged an insurgency against Turkey since 1984.
Turkey's military has carried out two incursions into Syria against the YPG militia, both focusing on its presence to the west of the Euphrates River.
President Tayyip Erdogan has signaled an impending operation against YPG forces the east of the river, delivering last month what he said was his "final warning" to those he said endangered Turkey's southern border with Syria.
The YPG spearheads the US-backed Syrian Democratic Forces in the fight against Islamic State in Syria. Washington's support for the militia has infuriated Ankara.Turkish forces last month bombarded YPG positions near Ayn al-Arab, Turkey's Anadolu news agency reported. It killed four Kurdish militants last week in a separate cross-border clash in the same region, broadcaster TRT reported.