At about 0430 GMT, Ida packed maximum sustained winds of about 75 miles (120 kilometers) an hour and north northwest at about 12 miles (19 kilometers) an hour, the Miami-based National Hurricane Center said.
The eye of the Category 1 hurricane was located about 120 miles (195 kilometers) southeast of Cozumel, Mexico, according to the center.
The storm is expected to dump up to 13 centimeters (five inches) of rain over parts of the Yucatan peninsula and Cuba, with possible isolated maximum amounts of 25 centimeters (10 inches).
The NHC warned rains could produce flash floods and mudslides in Central America and the Caribbean.
Thursday, Ida battered Nicaragua's Caribbean coast despite being downgraded to a tropical depression.
Heavy rains from Ida swelled Nicaraguan rivers, destroying an estimated 930 houses and hitting remote communities in one of Central America's poorest nations.
Around 13,000 people were left homeless following the deluge.
Nicaragua's government on Friday began distributing food, medicine and water to affected communities via army airplanes and boats.
But according to local media reports many victims of the storm in remote areas have yet to receive any relief and have been forced to sleep in outdoors after losing their homes.