The storm has already caused severe flooding and landslides that left 50 dead in El Salvador and hundreds homeless in Nicaragua.
Ida is currently about 100 miles (155 kilometers) north-northeast of Cozumel, Mexico, and is moving near 10 miles (17 kilometers) per hour, the NHC said.
A hurricane watch has been issued for parts of the Yucatan Peninsula, as well as for the area east of the Mississippi-Alabama border through the north-west area of Florida.
The NHC stressed that the hurricane watch does not cover the city of New Orleans, which was devastated in 2005 by Hurricane Katrina.