Tropical Storm Dorian could strengthen into a hurricane as early as Tuesday — as it continues to roar into the Caribbean with Barbados, Puerto Rico and the Dominican Republic in its path.

The storm, which was packing 60 mph winds by midday Monday, could be a Category 1 by the time it approaches Puerto Rico on Wednesday, the National Weather Service said — even as Barbados was bracing for high winds and downpours of up to 10 inches late Monday or early Tuesday.

Barbadian Prime Minister Mia Mottley ordered schools and government buildings closed on the island, and urged residents to remain indoors for their own safety.

“When you’re dead, you’re dead,” Mottley said in a televised address. “Stay inside and get some rest.”

The storm’s strength as it moves deeper into the Caribbean will depend heavily on its path over the next 48 hours, said Dan Kottlowski, senior meteorologist and lead hurricane forecaster for AccuWeather.

He said Hispaniola “is like a brick wall” for tropical storm systems because of its mountainous terrain, so Dorian would likely weaken if it hits the island head-on — reducing the storm’s damage in the rest of the Caribbean and along the US coastline.

But it could be a different matter if the storm dodges the islands and stays over water.

“If it goes between the two islands, then it could become a very powerful hurricane,” Kottlowski said. “That could really invite some major, major problems.”

Regardless, Kottlowski said Dorian is unlikely to have much of an impact in the Northeast — although it’s still a bit too early to tell for sure.

“The chance of Dorian affecting New York City is probably less than 1% right now,” he said. “But that could increase dramatically depending on how it interacts with Hispaniola.”

“This far out, I can’t tell you,” he said. “The crystal ball is not glowing right now for Dorian.”

With Post wires