The National Hurricane Center upgraded the tropical storm to a category 1 hurricane Tuesday night after wind speeds reached 75 miles per hour.
Alex is the first named hurricane of the year. The hurricane season officially starts June 1, and the storm's early arrival portends a busy season.
According to the National Hurricane Center, Alex is expected to make landfall later today or early Thursday, dropping six to 12 inches of rain on Mexico and southern Texas and up to as many as 20 inches in some places.
"These rains could cause life-threatening flash floods and mudslides especially in mountainous areas," the NHC said.
As of 4 a.m. CDT Wednesday, Alex was 235 miles off the coast, moving at around 7 m.p.h. with wind speeds of around 80 m.p.h.
President Obama issued an early disaster declaration for southern Texas counties late Tuesday.
Three oil rigs and 28 platforms in the Gulf have been evacuated, but Alex is expected to avoid the slick resulting from the ongoing Deepwater Horizon leak.
Wind and waves, however, have hampered oil cleanup efforts in the Gulf. Rough seas have caused oil collecting booms to wash ashore and authorities have stopped controlled burns on the surface.
Thousands of boats were kept in dock and beach cleaning crews, working along the Gulf coast, have contended with 25 mph winds whipping up sand and gobs of oil. The wind helped disperse some of the leaked oil, but heavy waves meant more oil is expected to wash ashore along the coast.
The National Weather Service is predicting an extremely active hurricane season this year, with an "85 percent chance of an above-normal season."
The weather service is predicting eight to 14 hurricanes and three to seven "major hurricanes."