In the nearby Turks and Caicos, wind and rain forced the closure of the airport and schools and cleared the streets.
There were no immediate reports of injuries or major damage.
Hanna is the eighth named storm of the Atlantic hurricane season and comes on the heels of Gustav, which was battering the Gulf Coast on Monday. An eventual strike on the U.S. mainland was in the forecast.
"Right now, the uncertainty is such that it could hit anywhere from Miami to the outer banks of North Carolina," said Jessica Schauer Clark, a meteorologist at the hurricane center. "So people really need to keep an eye on it."
NASA wasn't taking any chances - it announced a delay of at least a day in the planned move of the space shuttle Atlantis from an assembly building at Florida's Kennedy Space Center to the launch pad. The move had been scheduled for Tuesday in preparation for an October mission to the Hubble Space Telescope.
At 1:30 p.m. EDT, Hanna's center was located near Mayaguana Island, moving west-southwest at 5 mph (7 kms) with maximum sustained winds near 75 mph (120 kilometers per hour) and higher gusts.
Hanna was expected to bring up to 12 inches of rain to the Turks chain, a popular tourist destination with about 22,000 people. Tourists Jason and Carolina Volpi were out of luck as they tried to leave. The Providenciales airport was shut down and all flights were canceled. They couldn't get seats out until Thursday, too late to attend business meetings back in Italy.
"The situation is very frustrating," Jason Volpi, 36, said as they waited under darkening skies for a taxi back to their hotel.
The European Union said Monday it would give euro2 million (US$2.9 million) to help the recovery from Gustav, which killed 94 people. The money will pay for clean water, food, medical care, shelter and basic household items in Haiti, Cuba, Jamaica and the Dominican Republic. In Haiti, 8,000 people are in temporary housing after high winds and floods destroyed homes and farms.
AP Aerospace Writer Marcia Dunn contributed to this report.