It remains unclear exactly how many people were onboard the craft when it overturned, said US Coast Guard spokesman Ricardo Castrodad, who said that a “mass rescue effort” was being carried out.
“We’re looking to rescue as many people as we can and find as many survivors as we can,” he said on Thursday.
The overturned boat was initially spotted by a US Customs and Border Protection helicopter earlier in the day.
“If not for that, 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,” said Mr Castrodad.
“They found them early enough that we were able to coordinate a response.”
Officials say that eight of the rescued migrants taken to hospital were Haitian, although it is not known the nationalities of the other people onboard.
The boat was discovered around 11 miles north of the uninhabited island of Desecheo, which is located off Puerto Rico’s west coast.
It is the latest incident in a string of rescues of people fleeing Haiti and the Dominican Republic, say US officials.
The US Coast Guard and Dominican navy rescued 68 people in an area between Puerto Rico and the Dominican Republic on Saturday.
The Coast Guard says that in the last fiscal year, which ended on 30 September, it apprehended 1527 Haitians, 838 Cubans and 742 migrants from the Domincan Republic.