Athens: A Greek navy frigate fired on two drones approaching the ship in the Gulf of Aden on Thursday morning - one was shot down.
The second unmanned aerial vehicle then turned away, as reported by Greek radio (ERT), citing the Ministry of Defence in Athens. The frigate is continuing its mission, it added.
The frigate was escorting a merchant ship as part of the EU naval mission Aspides, which aims to protect merchant ships from attacks by the militant Islamist Houthi from Yemen.
The Gulf of Aden, off the Yemeni coast, links the Arabian Sea and the Red Sea.
Houthi militants have been attacking ships in the Red Sea region in what they say is retaliation for Israeli military action in the Gaza Strip.
Major shipping companies are increasingly avoiding the shortest sea route between Asia and Europe and sailing the much longer journey around South Africa's Cape of Good Hope instead.
The Iran-backed Houthi militia say they want to force an end to the Israeli attacks in Gaza, which followed the unprecedented massacre by the Palestinian Islamist organisation Hamas last October.
Several Western countries, including the United States and Britain, have launched operations to protect ships in the region in response to the Houthi attacks.
The European Union has also deployed a military operation to secure merchant shipping in the Red Sea.