Desmond McKenzie, the minister of local government and community development, gave an update on Tuesday evening as the storm's eye tracked off land.
McKenzie said that infrastructure had been "severely compromised", with more than 530,000 residents left without electricity as of 4pm local time, which equated to about 77 per cent of Jamaica Public Service Company customers across the island. "Jamaica's gone through what I can call one of its worst periods," he said.
There were "close to 15,000" residents in emergency shelters across the island, he said, adding: "We also noticed that there are communities where residents have gone and have created makeshift shelters."
The scale of damage in Jamaica is beginning to come into view after Hurricane Melissa became the strongest storm to strike the island in 174 years of record-keeping.
The storm took hours to cross over Jamaica, a passage over land that diminished its winds, dropping down to category 3 with winds of 125mph from the maximum level of 5.
Strong winds continued in Jamaica overnight, with hundreds of thousands left without power and many roads impassable.
The storm, which made landfall in Jamaica as a category 5, was one of the most intense seen in the Atlantic basin, meteorologists said, with a "textbook" structure and "hellacious" sustained winds of 185mph (298km/h) that wreaked crippling devastation.
"I have been on my knees in prayer," Andrew Holness, the prime minister, said. "There is no infrastructure in the region that can withstand a category 5."
Hurricane Melissa weakened to a category 3 storm before reaching Cuba on Wednesday, United States weather officials said.
"Melissa is expected to remain a powerful hurricane when it moves across Cuba and the Bahamas and passes near Bermuda," the National Hurricane Center said in its latest advisory.
The storm had been "re-strengthening" to a category 4 hurricane as it approached eastern Cuba, the agency had said on Wednesday before revising the storm down.