Iselle made landfall early on Friday morning on the chain's Big Island, shortly after it was downgraded from hurricane to tropical storm.
But Hurricane Julio, a Category 3 storm with winds of more than 120mph, is about 1,000 miles (1,609km) away.
Hawaiian officials have urged residents to stock up on emergency supplies.
The last cyclone to hit Hawaii, Hurricane Iniki in 1992, killed six and caused $2.4bn (Â£1.4bn) in damage.
Five to eight inches of rain are forecast, along with heavy winds and potential flash flooding in some parts of the state.
The storm was weakening as it hit the terrain of the eastern-most island of Hawaii, also known as the Big Island, according to Chris Brenchley, a National Weather Service meteorologist in Honolulu.
"As wind blows into the terrain, the terrain kind of redirects the wind," he said.
The state's department of emergency management has asked residents to prepare a seven-day emergency kit, including non-perishable food and water.
Hawaii's remoteness from the mainland makes it hard to get emergency supplies to the state. Stores have had to quickly restock bottled water and other supplies.
The storm has already knocked out power for more than 18,000 people on the Big Island, according to the Honolulu Star-Advertiser. Another 2,700 were without power on the island of Maui.
At least 50 flights from major airlines were canceled on Thursday and an inter-island airline cancelled all of its flights on Friday.
Rudy Cruz and Ashley Dochnahl from California told the Associated Press they had attempted to fly back early but failed to secure a flight.
"We were trying to beat it, but we now will have to ride it out," Mr Cruz said.
Big Island resident Andrew Fujimura said the waves were topping 20ft (6m) along the coast.
"I can't say I'm too worried," he said. "Worst-case scenario, the power may go out a day or two. But we're prepared for that kind of stuff out here."
A rare tropical storm battering Hawaii has already caused power blackouts and blocked roads on one island, but no deaths have been reported.