At 1200 GMT, Ida was located 220 miles (360 kilometers) off Grand Cayman Island and moving north at eight miles (13 kilometers) an hour, the Miami-based National Hurricane Center said.
Ida's winds strengthened to 45 miles (75 kilometers) an hour, which qualified it for tropical storm status, according to the center.
On Friday, Ida battered Nicaragua's Caribbean coast despite being downgraded to a tropical depression.
Heavy rains from Ida swelled Nicaraguan rivers, destroying an estimated 530 houses and hitting remote communities in one of Central America's poorest nations.
"They are estimating that 40,000 people will be directly or indirectly affected by the hurricane in preliminary damage projections," Jose Luis Perez, director of the Nicaraguan national disaster response corps, told AFP late Thursday.
The NHC warned rains could produce flash floods and mudslides in Central America and the Caribbean.
One of the first areas affected were the Corn Islands, a tropical paradise popular with backpackers. Around 300 tourists were evacuated from the islands by civil defense forces on Wednesday.