Hurricane Melissa weakened to a Category 2 storm that is expected to cause catastrophic damage as it passes through Cuba, a day after it hit Jamaica as one of the most powerful Atlantic storms on record.

The hurricane passed through eastern Cuba on Wednesday morning with 105 mile-an-hour winds and is expected to dump as much as 25 inches of rain in certain areas, according to the National Hurricane Center. The storm made landfall early Wednesday in the Cuban province of Santiago de Cuba with maximum sustained winds of close to 120 mph.

“This will cause life-threatening and potentially catastrophic flash flooding with numerous landslides,” the National Hurricane Center said.

Cuba’s president, Miguel Díaz-Canel , said more than 735,000 people were evacuated ahead of the storm.

Melissa pummeled Jamaica as a Category 5 storm Tuesday with winds of 185 mph. It downed power lines and cut off the internet, making it hard for the country to release information on the damage. Heavy rains, flash flooding and landslides are expected to continue in Jamaica on Wednesday, the National Hurricane Center said.

Hurricane Allen in 1980 remains the strongest Atlantic storm on record with peak sustained winds of 190 mph.

Forecasters expect that parts of Jamaica, an island of 2.8 million people, could be uninhabitable for weeks or months.

The storm slowed to a Category 2 hurricane as it made its way through the eastern Cuban provinces of Granma, Guantanamo, Holguin, Las Tunas and Santiago de Cuba.

Melissa is expected to remain a forceful hurricane as it moves out of Cuba and heads toward the Bahamas. The hurricane center warned people in the Bahamas to seek shelter. The storm is then forecast to pass west of Bermuda late Thursday night or Friday morning, with heavy rainfall expected.

Ahead of Melissa’s arrival in Cuba, the U.S. evacuated more than 1,000 people from Guantanamo Bay, a U.S. Navy base. Forecasters said flash flooding and landslides will hit parts of Haiti and the Dominican Republic through the middle of the week. Tropical storm conditions were expected in Haiti on Wednesday.

Write to Joseph Pisani at joseph.pisani@wsj.com