As of 1500 GMT, the storm was 90 miles (145 kilometers) south of New Orleans, moving northward at 12 miles per hour (19 kph), the NHC said.
In Washington, US President Donald Trump said he would be signing an emergency declaration for Louisiana, a measure that enables the release of federal aid.
Forecasters said Cristobal had strengthened in recent days, now packing maximum sustained winds of 50 mph with stronger gusts.
The NHC issued a storm surge warning -- meaning "a danger of life-threatening inundation" -- for the area from the mouth of the Mississippi River to Ocean Springs, Mississippi, about 90 miles away.
And it issued a tropical storm warning for an area extending to the Florida Panhandle, meaning high winds and heavy rainfall are expected within 24 hours.
The storm is expected to weaken as it moves north into Arkansas and Missouri on Monday and Tuesday.
Forecasters have predicted a heavier than usual Atlantic hurricane season.
Cristobal's formation early in the week marked the earliest that the hurricane season has seen its third named disturbance, US meteorologists said Tuesday.
Cristobal evolved from Tropical Storm Amanda, which left at least 26 people dead across Central America and provoked flooding and landslides.
Officials consider the Atlantic hurricane season to run from June 1 to November 30.
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