Cuban state television announced that all buses and trains to and from Havana were suspended, as was ferry service to the Isla de Juventud, the outlying Cuban island next in Gustav's path.
Authorities announced they were prepared to "protect" the 20,000 tourists in Matanzas province, which includes the famous beach resort of Varadero.
Gustav rolled over the Cayman Islands Friday with fierce winds that tore down trees and power lines.
At first light Saturday, Associated Press journalists found that Grand Cayman island was spared major damage. Big surging waves pounded at the island, but there was little flooding, and wind damage was limited because islanders had removed signs and other items that could blow away.
It was expected to cross Cuba's cigar country Saturday and head into the Gulf of Mexico by Sunday.
Gustav first struck Cayman Brac and Little Cayman, the smaller easternmost "Sister Islands" in the chain. Storm surge and heavy rains flooded the streets.
Two people were knocked down by huge waves as they tried to take pictures of the storm on Little Cayman, but there were no other immediate reports of injuries, said Hemant Balgobin, disaster manager for the Red Cross in the British territory.
"Things weren't really as bad as they could have been," he said.
More than 1,100 people spent the night in government shelters in the three islands as high waves and heavy winds battered the chain, the National Emergency Operations Center said in a statement. Most people hunkered down in private homes or hotels.
By early Saturday, Gustav's eye had left the Caymans behind and was about 225 miles (360 kilometers) east-southeast of the western tip of Cuba and just 85 miles (135 kilometers) east of the Isla de Juventud. It was expected to be moving northwest near 12 mph (19 kph).
The storm killed four people in a daylong march across the length of Jamaica, where it ripped off roofs and downed power lines. About 4,000 people were displaced from their homes, with about half relocated to shelters.
At least 59 people died in Haiti and eight in the Dominican Republic.