Police spokesman Keith Clarke said in today's update that authorities have accounted for only 16 of 69 people aboard the boat.
Officials say they've arrested one man and that an undetermined number of migrants made it to land.
The boat capsized on Tuesday near the northwest point of Providenciales island. It was carrying 50 men and 19 women.
The British Caribbean territory lies between Haiti and the Bahamas and has long been a favored destination and smuggling route for Haitian migrants.