The bodies of the migrants, including two women, were discovered in the western province of Aydin, the private Dogan news agency reported.
"Nine migrants were rescued while 11 migrants' bodies were taken from the sea," the coast guard said in a statement on its website.
"According to the rescued migrants' statements, it was learned that 20 people (migrants) were on the boat," it added.
One of those rescued was a baby who remained in a "critical condition", district governor Muammer Aksoy was quoted as saying by Dogan.
The boat capsized after strong waves and winds, Dogan reported, as it was probably attempting to reach the Greek island of Samos.
The deaths come less than a week after the first anniversary of an EU-Turkey agreement to halt migrant arrivals in Europe, which has sharply reduced the number of crossings to the bloc from Turkey.
But Ankara has raised alarms in Brussels by threatening in recent weeks to scrap the agreement, which came into force after an estimated 1.26 million migrants reached Europe in 2015.
According to the International Organization for Migration, there were around 363,000 migrant arrivals in Greece in 2016 after the Turkey-EU accord.
Under the deal, Turkey undertook to tighten its maritime borders and break up the people-smuggling networks that help migrants to make the risky crossing, in exchange for billions of euros in support for refugees in Turkey.
Ankara has also criticised the EU for failing to fulfil its promise to give visa-free travel in the Schengen zone nations to Turks as part of the agreement.
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