Nikos Lagkadianos, a coastguard spokesman, said 11 people were rescued from the sea between Lesbos and Turkey and one swam ashore in the early hours. The survivors said they thought 13 of their number were missing.
The girl was found unconscious and was declared dead later at hospital, Lagkadianos said, according to Reuters.
Tens of thousands of mainly Syrian refugees have braved rough seas this year to make the short but precarious journey from Turkey to Greece's eastern islands, mainly in flimsy and overcrowded inflatable boats.
Twenty-two migrants drowned and 200 more were rescued trying to reach the Greek island of Kos on Tuesday and 34 refugees, almost half of them babies and children, drowned when their boat sank off the small island of Farmakonisi last Sunday.
Of the record 430,000 refugees and migrants that have made the journey across the Mediterranean to Europe so far this year, 309,000 have arrived via Greece, according to the International Organization for Migration.
In July and August alone, Greece saw 150,000 arrivals, Greece's pre-election interim maritime minister, Christos Zois, told Reuters this week.