Schools and many businesses closed and shelters opened in anticipation of the storm, which was downgraded first to a Category 2 and then to a Category 1 hurricane with top sustained winds of 85 mph. The storm moved about 95 miles south of South Point, the southernmost area of the United States.
At 8 p.m. local time, the storm was moving to the west-northwest near 10 mph.
CBS Affiliate KGMB9 in Honolulu reports the the Big Island is still under a Hurricane Watch as well as a Tropical Storm Warning, meaning that hurricane conditions are possible within 36 hours and tropical storm conditions (winds at least 39 mph) are imminent within 24 hours.
The island is also under a Flash Flood Watch, through Wednesday, reports KGMB9, which means flooding conditions are possible but not yet imminent.
Aircraft reconnaissance found the eye of the hurricane had disappeared, an indication the storm continued to weaken, forecasters said.
The Central Pacific Hurricane Center in Honolulu said the Big Island could expect winds exceeding 40 mph and 10 inches of rain overnight and into Wednesday.
The storm comes on the heels of a 5.4-magnitude earthquake centered 25 miles south of Hilo. The quake Monday night caused a small landslide, but there were no reports of injuries or structural damage, said Tom Brown, a spokesman for Hawaii County Civil Defense.
More than two dozen aftershocks followed, the largest measuring magnitude 3.2, said Jim Kauahikaua, scientist in charge at the U.S. Geological Survey's Hawaiian Volcano Observatory.
Anticipating Flossie, the Federal Emergency Management Agency dispatched a 20-person advance emergency response team that arrived in Hawaii on Monday, spokeswoman Kim Walz said. The team includes specialists in areas of transportation, aviation, public works and health.
"Instead of waiting for an actual disaster and then going in and providing support, we want to be ready," she said. "We've begun to move resources into place ahead of time to be prepared."
The National Weather Service placed the Big Island under a hurricane watch and a tropical storm warning because of the storm, which was supposed to affect the island through Wednesday. A flash flood watch was also issued for the island.
Hurricane-force winds of at least 74 mph extended outward up to 40 miles from the center of the storm, while tropical storm force wind of at least 39 mph extend outward up to 105 miles.
"This is too close for comfort," said National Guard Maj. Gen. Robert Lee, the state adjutant general.
At South Point, resident Brianna Beck visited a favorite swimming spot to watch the waves. Her family prepared for the hurricane by taping the windows and tying down everything in their yard.