The girl was pulled from the sea by a patrol boat of the EU's border force agency Frontex but died in hospital in Kastelorizo, the coastguard.
Twenty of the 25 people rescued were picked up on the rocky coast of the island, which they had managed to swim to.
No details were released on the nationalities of those on board.
In 2015, around a million people undertook risky sea journeys to cross the Mediterranean to Europe, mostly to Greece from Turkey over the Aegean Sea.
Thousands died in the perilous crossing. Responding to international pressure, Turkey tightened its sea borders and cracked down on migrant smuggling rings as part of a 2016 deal with the EU.
The numbers of migrants crossing the Aegean has since dwindled.
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