Gonzalo strengthened to a "major hurricane" over the open Atlantic and was expected to continue gaining force, forecasters said.
Packing maximum sustained winds of 115 miles (185 kilometers) an hour, with gusts even stronger, Gonzalo surged to a Category Three on the Saffir-Simpson scale, the Miami-based National Hurricane Center said.
"Additional strengthening is forecast during the next 48 hours and Gonzalo is expected to become a Category Four storm on Wednesday," the NHC said.
The highest category on the Saffir-Simpson scale is five.
The storm skirted the Caribbean and was moving over open ocean, some 770 miles (1,240 kilometers) south of Bermuda.
No coastal warnings were in place, but forecasters cautioned Bermuda to closely monitor the storm's path.
Three people were reported missing in the islands of St. Martin and St. Barthelemy after the storm passed, and French authorities expressed concern about four other people they were trying to contact.
The missing were a man who fell off his boat in St. Martin and two others who were trying to get back to their boat in St. Barthelemy.
St. Martin is divided between French and Dutch sides, while St. Barthelemy is French.