Hurricane Hermine gained strength on Thursday evening as it roared toward Florida’s Gulf Coast, churning up pounding surf that battered docks and boathouses as people braced for the first direct hit on the state from a hurricane in over a decade.

The National Hurricane Center said the storm’s top sustained winds rose from 75 mph in the afternoon to 80 mph by nightfall as the former tropical storm gained new fury as it bore down on the coast.

Florida Governor Rick Scott warned of the danger of strong storm surge, high winds, downed trees and power outages, and had urged people during the day to move to inland shelters if necessary and make sure they had enough food, water and medicine.

“This is a life-threatening situation,” Mr. Scott said. “It’s going to be a lot of risk. Right now, I want everybody to be safe.”

Courtney Chason, a longtime resident of Carrabelle in the Big Bend coastal area, warily watched on Thursday evening as surging waves began battering some docks and boathouses, the angry surf slowly tearing at them. Water also crashed into yards closest to the shore.

“I’ve never seen it this high, it’s pretty damn crazy,” Mr. Chason said. “I hope it doesn’t get any higher; we need lots of prayers.”

A strengthened Hermine also sent heavy squalls with its outer bands over Gulf coast beaches elsewhere. By Thursday evening, the normally wide, sugar—sand beach on Treasure Island was entirely covered in water. Palm trees whipped in the wind. Elsewhere along the beach, folks stood gawking at the abnormally large waves and took selfies ahead of the storm.

The city of St. Petersburg was littered with downed palm fronds and tree branches, and low-lying streets were flooded.

In north Florida, some 9,200 power outages also were reported on Thursday evening on an outage map maintained by officials in Tallahassee, the capital city located in north Florida about 35 miles from the coast. Utility officials couldn’t immediately be reached for more details though Florida’s governor had warned some of the city’s stately trees might topple over power lines in storm winds.

Mr. Scott added that 6,000 National Guardsmen in Florida are ready to mobilize after the storm passes. The governors of Georgia and North Carolina declared states of emergency.

At 10 p.m. EDT, Hermine was centered about 65 km southeast of Apalachicola, Florida, while moving north-northeast at about 14 mph (22 kph). Forecasters said it had top sustained winds of 80 mph (130 kph) as a Category 1 hurricane.

Projected rainfall ranged up to 10 inches in parts of northern Florida and southern Georgia, with 4 to 10 inches possible along the coasts of Georgia and the Carolinas by Sunday. Lesser amounts were forecast farther up the Atlantic Coast, because the storm was expected to veer out to sea.

Florida’s governor ordered many state government offices to close at noon, including those in the Tallahassee, home to tens of thousands of state employees. The city has not had a direct hit from a hurricane in 30 years.

The last hurricane to strike Florida was Wilma, a powerful Category 3 storm that arrived on Oct. 24, 2005. It swept across the Everglades and struck heavily populated south Florida, causing five deaths in the state and an estimated $23 billion in damage.

Residents on some islands and other low-lying, flood-prone areas in Florida were urged to clear out earlier Thursday.

Flooding was expected across a wide swath of the Big Bend, which has a marshy coastline and is made up of mostly rural communities and small towns, where fishing, hunting and camping are mainstays of life.

On Thursday, residents were out in force preparing for the storm, and stores began running low on bottled water and flashlights. City crews struggled to keep up with demand for sand for filling sandbags.

On Cedar Key, a small island along the Big Bend, about a dozen people went from storefront to storefront, putting up shutters and nailing pieces of plywood to protect businesses from the wind.

One of them, Joe Allen, spray-painted on plywood in large black letters- “Bring it on, Hermine.” Despite the bravado, he said, “I’m worried. You can never fully protect yourself from nature.”

Chris Greaves and family members stopped in Tallahassee to pick up sandbags for his garage and the church they attend. Mr. Greaves said he lived in South Florida when Hurricane Andrew devastated the area in 1992. While he said he doesn’t expect the same kind of widespread damage, he warned that tropical weather is “nothing to mess with.”