The sailing boat carrying the migrants ran aground on rocks off the Aegean island on a crossing from Turkey, a police spokesman told AFP.
Most of the survivors had to be pulled from the sea, and police fear the death toll could yet grow as they try to determine how many people were on board.
Of those rescued, "57 are safe and sound and 23 were taken to hospital in Rhodes," he said.
There has been a surge in migrants trying to reach Greece's Aegean islands from the Turkish coast in the last 10 days.
Greece's radical left government, which has taken a less hardline attitude to migrants than its predecessors, appealed to local authorities last week to help accommodate the latest wave of refugees.
Greece lacks the means and the infrastructure to adequately cope with the growing number of migrants landing on its shores and crossing its borders, most of them en route to northern Europe.
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