Alex, the first named storm of the 2010 Atlantic hurricane season, is expected to weaken as it moves inland over Belize and the Yucatan Peninsula overnight, the Miami-based centre said.
But the NHC added "strengthening is forecast on Sunday night as Alex moves over the southern Gulf of Mexico".
Forecasts predict the hurricane will then turn into a small one later in the week as it moves between the northern coast of Mexico and southern coast of Texas.
Earlier on Saturday, in the Mexican state of Quintana Roo, authorities had evacuated about 200 people from villages across the Chinchorro reef, near Belize.
In Chetumal, the capital of the state of Quintana Roo across the border with Belize, heavier rain and winds arrived in the early hours of Sunday.
Some rain fell over Cancun, a major seaside resort that draws visitors from around the world, but there was no threat to some 35,000 tourists in the area, authorities said.
A tropical storm warning has been issued for the coast of Belize and the east coast of Mexico's Yucatan Peninsula from Chetumal to Cancun.
It is expected that Alex will bring 10 to 20cm of rain through Sunday evening.
The Atlantic hurricane season runs from June 1 to November 30 and meteorologists predict this year will be a very active one.
Hurricanes gain strength from warm water and the sea temperatures in the tropical Atlantic have been higher than usual this year.