A state of emergency has been declared in the US territory as residents prepare for Dorian to bring the first hurricane of the season.
The National Hurricane Centre said the storm already has sustained winds of up to 50mph and is forecast to strengthen over the next 48 hours.
Officials have also issued tropical storm warnings for Martinique, St Lucia, and St Vincent and the Grenadines.
Barbados was hit by strong winds, rain and thunder and lightning on Monday night as Dorian passed, and residents were urged to remain indoors amid reports of power cuts.
The storm appeared to have caused little damage, however home affairs minister Edmund Hinkson urged residents to remain vigilant, adding: “We are not out of danger yet.”
By Tuesday morning the storm was about 30 miles southeast of St Lucia, blowing sustained winds of up to 50mph.
Officials warned it could become a hurricane by the time it passes the southwest side of Puerto Rico on Wednesday.
Hundreds of people in Puerto Rico have been stocking up on supplies at supermarkets and fuel stations in preparation for the storm.
Many are worried about power outages and heavy rains on an island still struggling to recover from Hurricane Maria, a Category 4 storm that hit in September 2017.
Some 30,000 homes still have blue tarps as roofs and the electrical grid remains fragile and prone to outages even during brief rain showers.
Puerto Rico governor Wanda Vazquez Garced declared a state of emergency for the US territory late on Monday.
She added that there would be about 360 shelters open across the island.
A new tropical depression also formed between the US eastern coast and Bermuda on Monday.
It was located about 320 miles southeast of Cape Hatteras in North Carolina and was moving east at 3 mph with maximum sustained winds of 35 mph.
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It was expected to become a tropical storm by Tuesday night.
The storms came just days after reports emerged of president Donald Trump suggesting nuclear weapons should be fired into hurricanes to stop them hitting the US.
A source in Washington alleged the US president raised the idea of bombing hurricanes with senior Homeland Security and national security officials on numerous occasions, dating back as far as 2017.
However Mr Trump later tweeted that the reports were “ridiculous” and “just more fake news”.
Agencies contributed to this report.