The owner of one of Cuba's best-known tobacco farms, the Robaina farm, published images showing the property's roofs smashed to the ground, destroyed greenhouses and wagons overturned.
"It was apocalyptic, a real disaster," wrote Hirochi Robaina, grandson of the operation's founder, on social media.
The island's main international airport -- José Martí, in Havana -- ceased operations Monday night.
Leaders of the Cuban-American community in Florida signed a petition Monday asking the owners of the island's largest hotels to offer lodging to Cuban families "who will be left homeless as a result of Ian."