The Royal Bahamas Defense Force says a patrol boat stopped the vessel west of Ragged Island.
Among the migrants were 23 women and three children. All were taken to a military base in Nassau for further investigation. The Bahamas usually repatriates migrants who are detained at sea.
A Defense Force statement says eight Cubans were also apprehended earlier this month in a vessel off Grand Bahamas.
The force has detained about 1,000 migrants so far this year.