Lala's maximum sustained winds increased to 120 km/h, the hurricane centre reported, making it a category one hurricane.
It was located about 135km south-southeast of South Point, Hawaii, on a forecast track that would take its eye over or near the island's southern end later on Saturday.
The National Hurricane Centre issued a rare hurricane warning for the Big Island, which hasn't experienced a direct hurricane landfall in 155 years.
Forecasters said higher elevations could get as much as 63.5cm of rain.
That could cause life-threatening mudslides in a mountainous area where people live off the grid in improvised housing, and authorities urged them to find safe shelters quickly.
"This is an enormous storm," Governor Josh Green said.
Tropical storm-force winds extended outward for as much as 350km, and were expected to hit the islands of Oahu and Kauai by Sunday morning.
Destructive flooding and even wildfires kicked up by the strong winds were possible across the island chain.
Mike Caputo, who lives in Keaau, near the east coast of the Big Island, said the main concern is flash flooding and fallen trees, especially albizia, a common tree.
"They're not very sturdy but they grow extremely large," Caputo, 50, a local fire captain, said.
"They can make roads impassable."
Tropical storm warnings were issued for the islands of Maui, Molokai, Lanai, Kahoolawe, Oahu, Kauai and Niihau.
According to a University of Hawaii atmospheric scientist's research of newspaper accounts, a category three hurricane hit the northeast corner of the Big Island in 1871.
The latest forecast has Lala striking "very close to the southern tip of the Big Island," said Vanessa Almanza, a weather service meteorologist in Honolulu.
State politician Jeanné Kapela urged people to remain alert.
"If you feel now that your house doesn't have a great roof or might not be able to withstand hurricane-force winds, then first things first you go to a family or friend's house and you kind of hunker down there," she told The Associated Press.
"We're hopeful the storm moves through quickly, but we're preparing for whatever comes."
Many Hawaiians are still dealing with the aftermath of devastating flooding in March.
Farmers and growers still recovering are worried about suffering more damage, according to Hawaii Farm Bureau.