The storm, last observed northwest of the island of Guadalupe and carrying maximum winds of 75km/h, could strengthen into a hurricane by Thursday after passing over Puerto Rico and veering north into the Atlantic, the US National Hurricane Center said.
Ernesto - the fifth named storm of the season - is expected to miss Florida and the US southeast, which are still reeling from Tropical Storm Debby.
Joseph Niskar, a lawyer who moved to Puerto Rico from Michigan after Hurricane Maria struck the island in 2017, is anticipating extended periods of time without water or electricity, much like many on the island experienced during Hurricane Fiona in 2022.
"I bought a generator big enough to run my refrigerator and fans to keep cool but will need gasoline that can be hard to get because a lot of people wait until the last minute and there can be long lines," Niskar said.
Last week, slow-moving Debby hit Florida's Gulf Coast as a Category one hurricane before soaking some parts of the Carolinas with up to 0.6m of rain.
Like Debby, Ernesto's greatest threat is torrential rain, which could spur flash floods and landslides, especially in the mountainous interior of Puerto Rico and nearby Caribbean islands.
On Monday, Puerto Rico Governor Pedro Pierluisi activated more than 200 National Guard members and expedited food benefits for families ahead of the storm's arrival.
Government workers were given the day off, with the exception of essential personnel.
Officials also postponed the first day of school from Tuesday to later in the week.
Schools in the Virgin Islands were also shut down.
Puerto Rico, with its fragile power grid, has a history of highly destructive storms.
In 2022, Hurricane Fiona knocked out power for about 80 per cent of the island's customers.
Five years earlier, Hurricane Maria plunged the territory into darkness.
LUMA Energy, the private operator of Puerto Rico's transmission and distribution system, said on X it had activated its emergency operations, mobilised crews ahead of the storm and advised residents to brace for power outages.
The storm is expected to cross parts of the Leeward Islands, which include Martinique, on Tuesday, reaching the US and British Virgin Islands and Puerto Rico by evening.
