Four women and a child have died after their boat capsized off the Greek island of Samos.
They are thought to be the first deaths in the area since a new deal with Turkey came in to force on Monday with the aim of deterring migrants.
Five other people were saved and a search is under way for four more.
This week, dozens of migrants were returned to Turkey under the new deal with the EU, which has been criticised by human rights groups.
Survivors from the latest drowning told officials that they were travelling on a 3.5-metre (11.5ft) vessel made of plastic.
On Friday, two ferries carrying more than 120 people, mostly Pakistanis, arrived in western Turkey from the Greek island of Lesbos.
More than 200 people were sent back on Monday, but returns have been stalled by a surge of asylum applications in Greece.
The EU-Turkey deal aims to ease the uncontrolled mass movement of people into Europe.
Under the new agreement, migrants who have arrived illegally in Greece since 20 March are expected to be sent back to Turkey if they do not apply for asylum or if their claim is rejected.
For each Syrian migrant returned to Turkey, the EU is due to take in another Syrian who has made a legitimate request.
Human rights organisations have attacked the scheme as badly flawed, warning that Turkey is not a safe place to return people.
Amnesty International reported that there was just one official who was processing applications on the island of Chios, and out of 833 claims that had been filed, he had processed only 10.
in 2016, up to 7 April
37% of 2016 arrivals are children
53% arrive on Lesbos
366 died on Turkey-Greece route
853,650 arrivals in 2015
There are meanwhile worries in Italy that migrants deterred from trying to reach Greece might try to enter the EU from North Africa instead, using the sea route from Libya to Italy.
“We are concerned because it’s predictable that this summer, maybe hundreds of thousands of people will arrive from Syria and African countries through Italy going to Europe,” Giorgia De Acutis of the Italian Red Cross told Reuters news agency.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.