Gonzalo strengthened to a "major hurricane" over the open Atlantic late Tuesday 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.
It was expected to continue moving northwest at 13 miles (20 kilometers) per hour.
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.
The storm caused property damage on both islands, which were battered by strong winds and heavy rains.
In St. Barthelemy a plane flipped on the airport's runway, while roads were blocked by fallen trees and telephone and power lines were torn from the ground.
A Category Four hurricane can cause major damage and leave cities and towns uninhabitable for weeks, with wind speeds reaching up to 156 miles (251 kilometers) per hour.
Gonzalo is the seventh storm of the Atlantic season -- which stretches from June to November -- and the third hurricane to slam the Caribbean this year.
Hurricane Cristobal left at least four people dead in late August when it trashed the Bahamas, Turks and Caicos Islands and Dominican Republic with heavy rains causing serious flooding.
In September, Hurricane Edouard remained too far from land to cause any serious damage.
The NHC said it believes storm activity will be lower than average this year.