The coast guard said the incident occurred on Friday while the speedboat was carrying out "dangerous manoeuvres" to try to evade a patrol vessel, causing migrants to fall into the sea.
Eighteen of the migrants were rescued.
Rescue workers on three coastguard vessels and a helicopter were working near the resort area of Afantou Beach in the northeast of the island.
It was unclear whether other passengers were missing, authorities said.
Eight of the survivors have been hospitalised, local officials said, with one of them in critical condition, according to state-run television.
Rhodes, one of several large Greek islands located near the coast of Turkey, is on a busy illegal smuggling route in the eastern Mediterranean.
At the main port of the island, police and ambulance workers held up sheets of grey tarp as the recovered bodies were carried into an ambulance.
It was the second deadly incident involving migrants in the past week, as authorities in Athens brace for a spike in arrivals as a result of wars in the Middle East.
Seven migrants were killed and dozens are believed to be missing after a boat partially sank south of the island of Crete at the weekend - one of four rescue operations during which more than 200 migrants were rescued.
The search south of Crete around the tiny island of Gavdos was called off Wednesday.
The number of migrants travelling illegally to Greece is expected to top 60,000 this year, with Syrians making up the largest number, followed by Afghans, Egyptians, Eritreans and Palestinians, according to government data.
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