"A serious incident occurred off the island of Symi when a yacht carrying 70 migrants from Turkey's western shores tried to illegally enter (Greek waters)," the marine ministry said in a statement.
Greek port police and officials from the EU border agency Frontex managed to halt and board the boat.
Shots were fired during scuffles between the police and three Turkish suspected people smugglers, the ministry said.
One of the suspected smugglers, who were all arrested, admitted to injuring an officer after grabbing his pistol, the statement added.
The dead migrant was "probably killed by gunfire", a doctor at Symi health centre was quoted as saying.
An investigation into his death has been launched. No details on his origin were given.
Marine Minister Christos Zois expressed sadness over the youth's death while praising the police for their "daily struggle in difficult conditions to aid migrants".
Greece is struggling to cope with the arrival of unprecedented numbers of people seeking refuge in Europe, mostly asylum-seekers fleeing wars in the Middle East and Asia.
Over 160,000 migrants have landed on Greece's shores so far this year.
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