The coast guard said 36 survivors were found on a rocky shoreline while three others were rescued earlier.
The victims were two women and six children, the daily newspaper Kathimerini reported.
A total of about 50 people are said to have been onboard.
So far, 36 people were able to save themselves on the shore of the island and the coastguard was searching for more passengers by boat.
Strong winds prevailed in the region at the time of the accident.
Accidents involving migrant boats, which are often unseaworthy barges or heavily overcrowded rubber dinghies, occur repeatedly in these waters.
Compared with last year, the number of migrants trying to reach Greece has significantly increased this year.
While there were fewer than 49,000 arrivals in 2023, about 54,000 migrants had already arrived in Greece by November 17, according to the United Nations High Commissioner for Refugees (UNHCR).
The registration camps on the islands of Samos, Kos, Leros, Lesbos and Chios are currently almost full.
They have a total capacity of about 14,000 places, of which almost 13,000 are occupied.
with AP
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