Wilma is the 21st named storm of the season. The only other time that many storms have formed since record-keeping began 154 years ago was in 1933.
At 11am EDT (4pm Irish time), Wilma had top sustained wind near 45mph the National Hurricane Centre said centred 220 miles south-southeast of Grand Cayman but expected to turn west.
A tropical storm warning was posted for the coast of Honduras. Over the weekend, a hurricane watch was posted in the Cayman Islands.
Long-term forecasts show the storm heading into the Gulf of Mexico by the weekend. Forecasters said conditions were favourable for it to become a significant hurricane.
Hurricane specialist Stacy Stewart said Wilma had shifted west and could hit Mexico’s Yucatan Peninsula. “At this time it doesn’t appear it will be a major threat to the United States during the next five days,” she said.
But Wilma is then expected to re-emerge into the Gulf and could become a threat to the southern US.
“Usually when a storm gets into the Gulf, it’s going to hit somewhere,” said hurricane centre meteorologist Larry Lahiff.
The US Gulf Coast was already battered this year by Hurricanes Katrina, Rita and Dennis.
Since 1995, the Atlantic has been in a period of higher hurricane activity. Scientists blame a rise in ocean temperatures and a decrease in vertical wind shear that rips hurricanes apart. Others argue that global warming is the culprit.
The six-month hurricane season ends on November 30. Wilma is the last on the list of storm names for 2005; there are 21 names each year because the letters q, u, x, y and z are skipped. If any other storms form, letters from the Greek alphabet would be used.
That has never happened yet.