Additional strengthening is forecast through Wednesday, when the eye of the storm is expected to be out in the open Atlantic.
The system is now located about 165 miles east-northeast of Cape Canaveral in the U.S. state of Florida.
The distribution of meals in Grand Bahama was reduced ahead of the storm, and a spokesman for the United Nations World Food Program said all flights into its logistics hub in Marsh Harbor in Abaco were suspended.
Late Sunday, Humberto strengthened to a Category 1 hurricane with maximum sustained winds of 75 miles per hour (120 kph).
Tropics active, Humberto likely to become hurricane: There's a few areas to watch in the tropics over the next couple of days.
There were concerns Humberto could bring unsafe weather conditions to Bahamas, where hundreds are still missing after Hurricane Dorian hit the islands earlier in September.
Its swells could still affect the coasts of Florida, Georgia, South Carolina and North Carolina in the coming days.
Currently, no coastal advisories have been issued in the Southeast.
A look at the wind speeds of each category of a hurricane.
Thousands of victims of Hurricane Dorian crowded into shelters as a tropical cyclone carrying heavy rain and strong winds threaten the already devastated Bahamas. Hurricanes that are Category 3, 4 or 5 are considered major hurricanes capable of causing devastating or catastrophic damage. Humberto is moving away from the northern Bahamas and staying well offshore of the Florida coast. Over the next five days however, the wave east of the Lesser Antilles has a 70 percent to become a tropical depression. Humberto is now whipping out winds of 65mph as it moves north at 7mph.
Although Hurricane Humberto will have no direct impact on the United States, the storm is taking aim at Bermuda and could bring rough surf and risky rip currents to the eastern U.S.