The survivors included 20 men and 11 women.
The "suspected illegal migrant voyage" overturned near an uninhabited Puerto Rican island and was spotted by a U.S. Customs and Border Protection officer from a helicopter late Thursday morning.
The rescue operation is expected to continue through the night for any more potential survivors as the Coast Guard isn’t sure how many people were on board.
"We're looking to rescue as many people as we can and find as many survivors as we can," Coast Guard spokesman Ricardo Castrodad said.
Castrodad said if the CBP officer hadn’t seen the boat "we would not have known about this until someone would have found any sign or received reports from people that their loved ones are missing. They found them early enough that we were able to coordinate a response."
The victims and survivors were non-U.S. citizens, the Coast Guard said, and included eight Haitians who were hospitalized, but the nationalities of the others have not been reported.
"Our hope and prayers are with the survivors and those still missing," Rear Admiral Brendan C. McPherson said in a statement. "Our highest priority is saving lives and that is what my crew will exhaust themselves doing. We are searching for survivors with all available assets, including helicopters, airplanes, and rescue boats from the U.S. Coast Guard, Customs and Border Protection Air and Marine Operations, and Puerto Rico Joint Forces of Rapid Response partners. We are continuing with shoreline responders to evacuate anyone who needs medical care ashore. The sea is dangerous. These ventures are dangerous."
The capsizing comes less than a week after the U.S. Coast Guard and Dominican navy on Saturday rescued 68 migrants in the Mona Passage, a treacherous area between Puerto Rico and the Dominican Republic. One woman believed to be from Haiti died, Castrodad said.
In the last fiscal year, which ended in September, more than 3,000 Haitians, Cubans and Dominicans were detained in the region attempting to make the crossing and human smuggling boat attempts have increased since then, authorities said.
The Coast Guard says the last several months since October have been the busiest for migrant boat interceptions since 2004.
Haitians are fleeing the country’s increase in gang violence and kidnappings in the last year.
The Associated Press contributed to this report.