Hurricane Paula has now reached Category 2 strength in the Caribbean.
The storm roared off the resort town of Cancun on Wednesday without any reported major damage before it was expected to veer northeast toward the island nation of Cuba.
Some flights out of the Cancun airport have been cancelled.
The Category 2 storm, with maximum sustained winds of 100 mph , swiped at the island of Cozumel and Isla Mujeres overnight on a northward advance and was about 55 miles east of Cancun around dawn Wednesday.
The U.S. National Hurricane Center said Paula was expected to shift to the northeast and weaken slightly on a course that would carry it into western Cuba by Wednesday night or early Thursday.
Forecasters say the western part of Cuba could be targeted by Paula, which was expected to feel tropical-storm-force winds by the afternoon.
One U.S. tourist has died as a result of the storm. Quintana Roo Mexican state prosecutors said in a statement that a U.S. man drowned when he went swimming in heavy surf near his hotel. Mickey Goodwin, a 54-year-old Texas resident, ignored warnings and red flags alerting the dangerous waters, the statement said.