The majority of victims were female and were found near the northwest point of Providenciales island, police spokesman Keith Clarke told The Associated Press.
The boat was carrying 69 people, and officials said the US Coast Guard is helping with an ongoing search for possible survivors.
"This is a tragic incident with significant loss of life," said Police Commissioner James Smith, who extended condolences to the victim's families.
Police said in a statement that they arrested a 23-year-old Haitian man who told them the single-engine boat left Haiti's north coast on Sunday and was carrying 50 men and 19 women. He said he swam to land after the boat struck a rock near the Turks & Caicos Islands early Tuesday and began to sink, police said.
"Whilst we are saddened at this great loss of human life, measures must be put in place to protect persons from themselves, potential victims from human traffickers and our borders from breaches by illegal entrants," she said. "Firm policy positions will be taken and strict enforcement of the laws of these lands will follow.
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