Several airlines, including British Airways, American Airlines and Air Jamaica said they were cancelling flights to the capital, Kingston, and visitors have been advised to delay travel plans to the island.
Seven people have been killed since the government announced last week that it was putting up fuel prices by almost a third to raise cash for spending on roads and public transport.
The continuing looting and vandalism led the Jamaican authorities to impose a curfew in Kingston for a second night on Wednesday. Damage to the island's economy has already been estimated in the millions of dollars.
Fuel running low
Schools, business and banks have been advised to remain closed and some petrol stations are reported to be running out of fuel.
Opposition marches on Wednesday passed off peacefully
A BBC correspondent in Kingston, Carol Orr, says most of the violence was contained in key troublespots in the city's central district and the neighbouring parish of St Catherine, where police, attempting to remove blockades, battled with men armed with guns, stones and in one instance bottle bombs.
On Wednesday evening thousands of people attended rallies and marches across the island organised by the opposition Jamaica Labour Party to call for the new fuel taxes to be scrapped and for Prime Minister PJ Patterson to step down.