FAJARDO, Puerto Rico—Hurricane Maria barreled into the eastern Caribbean late Monday as a dangerous Category 5 storm, ripping roofs from homes, knocking out electricity on the island of Dominica and threatening others in the region already ravaged by Hurricane Irma.

The storm made landfall in Dominica around 9:15 p.m. ET, with maximum sustained winds near 160 miles an hour, according to the U.S. National Hurricane Center. The storm is expected to move toward Puerto Rico and the Virgin Islands late Tuesday and Wednesday.

The hurricane center said that while some fluctuations in intensity are likely in the next day or two—with Maria briefly downgraded to a Category 4 storm before being raised again early Tuesday—the storm is forecast to remain extremely dangerous.

Dominica Prime Minister Roosevelt Skerrit said in posts on his Facebook page that the strong winds ripped the roof off his house, and that the house was flooding, adding shortly afterward that he had been rescued.

“The winds are merciless! We shall survive by the grace of God,” he posted.

In another post early Tuesday he said initial reports were of “widespread devastation” and that “so far we have lost all what money can buy and replace.” Mr. Skerrit said his focus was now on rescuing the trapped and securing medical assistance for the injured, fearing possible deaths as a result of likely landslides.

On Monday, the prime minister had urged people in flood-prone areas to move to safety with friends or relatives, or into shelters.

“This is not a time for heroism,” he said at a press conference.

Several callers to Dominica radio reported strong winds and rain, and loss of electrical power and damage to roofs.

Puerto Rico Gov. Ricardo Rosselló has said the storm posed a “serious menace” to the island. Officials on the outlying islands that Maria is expected to slam first also issued warnings Monday.

Although Maria is currently tracking south of the islands devastated by Hurricane Irma two weeks ago, tropical storm-force winds and rain are expected to hit St. Martin and the U.S. Virgin Islands this week.

Maria’s current path is expected to take it 22 miles south of St. Croix, the southernmost U.S. Virgin Island that was largely spared the previous storm’s wrath.

But Gov. Kenneth Mapp of the U.S. Virgin Islands warned residents Monday that the storm could easily shift direction. Even tropical storm force-winds and rain can cause a lot of destruction, especially on St. Thomas and St. John, which suffered heavy damage from Irma.

“Just remember this is a live animal,” Mr. Mapp warned the territory’s 105,000 residents in a televised briefing. “Do not take any comfort at this point that we are going to be out of hurricane-force winds.”

“At the end of the day, my friends, this is still going to be a very dangerous hurricane,” he said.

Hurricane Maria is aimed directly at the islands that were expected to pick up much of the cruise ship and other tourism business lost on Anguilla and St. Martin.

Forecasters were warning of hurricane conditions for Guadeloupe, Dominica, Martinique and St. Kitts, Nevis and Montserrat on Monday. They advised Puerto Rico, where electricity remains off in some areas because of Irma’s glancing blow, to monitor the storm closely.

“We are screwed,” said Luis Díaz, who operates a taxi service in Fajardo, a port town on Puerto Rico’s northeastern coast. He said Maria’s trajectory was similar to Hurricane Hugo, which devastated the island in 1989, leaving parts of Puerto Rico without power for seven months.

Predicting as much as a foot of rain in some places, the National Hurricane Center said Hurricane Maria’s “rainfall on all of these islands could cause life-threatening flash floods and mudslides.”

Irma, a Category 5 storm when it slammed into the northern Caribbean early this month, killed at least 38 people on the islands, damaged or destroyed as much as 90% of the homes and other buildings in some places and stripped the land bare of lush tropical foliage.

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Maria’s approach raised the anxiety level over the weekend among residents of the Virgin Islands and others hit by Irma, many of whom have been nearly two weeks without electricity and roofs. Many of the aid flights and boats bringing food, water and other supplies to the stricken islands have been launched from Puerto Rico.

“We’re being vigilant. We have systems, we have experience and we have strength. We also have faith,” Hugh Riley, secretary-general of the Barbados-based Caribbean Tourism Organization, said as Maria approached the Leeward Islands.

“Protecting ourselves and our guests is now today’s priority,” said Mr. Riley, whose organization represents hotels and other businesses on the vulnerable islands. “Tomorrow we’ll resume the cleanup and rebuilding process.”

Meanwhile, Hurricane Jose, which had threatened the northern Caribbean a few days after Irma before turning north into the Atlantic, is moving slowly offshore of the central U.S. Atlantic Coast. Although they expect Jose to remain at sea, forecasters are warning of dangerously heavy surf along the New Jersey coast northward in the coming days.

People in the tiny two-island nation of Antigua and Barbuda, the first to be hit by Irma, were busy preparing for the possible impact of Maria.

Nearly all of Barbuda’s 1,800 residents had already been evacuated 25 miles south to Antigua and remain there, staying in government shelters or with friends and relatives, Philmore Mullin, the director of emergency response, said Sunday.

“We’re keeping a very close eye on Maria and making preparations,” Mr. Mullin said.

On St. John, one of the U.S. Virgin Islands worst hit by Irma, a feeling of dread was palpable at a town hall meeting Saturday to discuss relief efforts in the wake of Irma and the new storm.

“We are strongly encouraging the residents of St. John who are able to do so to evacuate,” said Ryan West, a spokesman for Love City Strong, an ad hoc citizen’s group that has played a key role in organizing boat evacuations from St. John and disaster relief to the island from Puerto Rico after Irma.

Some people at the meeting gasped while others sat in stunned silence. “It’s a slap in the face,” said one woman in flip-flops.

The island is a favorite winter gathering place for vacationing millionaires and independent-minded sail boat skippers.

“I feel very fearful for my husband,” said Tonia Lovejoy, 37 years old, who left Saturday with her 4-month-old daughter on a Puerto Rico-bound boat. Her husband stayed behind to repair the couple’s 36-foot sailboat on which they live. “If another storm is coming, he should leave. We are already living on a thin thread,” she said.

“This is bad,” said Stephen Tilas, a 51-year-old property manager who changed his plans after hearing about Maria’s threatening trajectory. Instead of beginning to repair the damaged villas he oversees, Mr. Tilas again closed his own house to prepare for the new storm.

—Anthony Harrup contributed to this article.

Write to Dudley Althaus at Dudley.Althaus@wsj.com and José de Córdoba at jose.decordoba@wsj.com