According to the Ekathimerini newspaper, this is not the first case of offensive behaviour by the Turkish military on the border. Earlier in the week, a Greek border guard reportedly came under fire from the Turkish side.
The Greek border police have been on high alert over a possible influx of undocumented migrants after Turkish President Recep Tayyip Erdogan opened the country's border with the European Union.
Ankara announced in late February that it would not be able to stem the flow of migrants and refugees following renewed violence in Syria's Idlib province, and therefore would open its borders with the EU to those wishing to cross.
Soon after, Turkey's borders with Greece and Bulgaria were flooded with thousands of migrants. Erdogan said earlier on Wednesday that Turkey would not close its borders with the EU for migrants until the bloc has fulfilled its promises.