The 17-year-old was seven months pregnant and also had cardiovascular problems, according to a statement from the country's health department.
Health officials could not be reached for comment, and no other details were available.
The country has confirmed 44 swine flu cases, and officials have said the vast majority of patients did not require hospitalisation.
Barbados, Cuba, Jamaica and Trinidad and Tobago are among the other Caribbean countries that have reported cases.
The disease has spread to 69 countries.
A vast majority of the nearly 22,000 cases reported so far have been mild, though 126 people have died.