A reconnaissance plane Saturday found the storm about 295 miles south-southeast of Santo Domingo, Dominican Republic, and 590 east-southeast of Kingston, Jamaica.
Ernesto was approaching the island nation at about 18 mph with maximum sustained winds of about 50 mph, the National Hurricane Center said in an 11 a.m. EDT statement.
Tropical storm force winds extend out 105 miles.
Forecasters said the center of the storm should pass south of Jamaica Sunday evening and move into the northwestern Caribbean Sea.
No strengthening of the winds is expected Saturday, although the hurricane center said they may increase Sunday to hurricane force.