Hurricane Alex caused severe flooding that killed at least two people and forced thousands of others to flee coastal fishing villages before weakening to a tropical storm over northern Mexico on Thursday.

A man gathers wood from a destroyed home after Hurricane Alex hit Playa Bagdad, 37 kilometres east of Matamoros in northeastern Mexico, near the Texas border. The dry Santa Catalina riverbed that cuts through the city of Monterrey roared to life, sweeping away cars and parts of rickety, wooden homes built along its path.

One man died when he was caught by a torrent of water along a six-lane highway, city civil protection director Pedro Trevino told the Televisa Monterrey network. The body of another man was found drowned by the side of a creek.

Nuevo Leon state Gov. Rodrigo Medina de la Cruz ordered all schools closed and appealed for people to stay home from all but essential jobs.

The Atlantic season's first hurricane largely spared nearby Texas, which had prepared for a direct hit. While Alex brought rain, spawned two tornadoes and forced the evacuation of 1,000 people from low-lying areas, state officials reported no injuries or major damage.

Earlier, Alex whipped up high waves that frustrated oil-spill cleanup efforts on the other side of the Gulf of Mexico and delivered tar balls and globs of crude onto already soiled beaches.

The storm made landfall Wednesday night on a sparsely populated stretch of coast in Mexico's Tamaulipas state, about 180 kilometres south of Brownsville, Texas, and Matamoros.

Much of Matamoros was flooded Thursday morning, said Saul Hernandez Bautista, the city's director of civil protection. He said at least 400 neighbourhoods were flooded, some with 30 centimetres of water and at least 2,500 people were in shelters, mostly people evacuated from lowing lying regions outside the city.

Trees were uprooted and electrical posts were down. Hernandez said there were no known injuries or deaths in the Matamoros area but he did not know about the area farther south where the eye of the storm hit.

"The damages are incalculable," Hernandez said. "The city is practically under water. But the most important thing is that there was no loss of life. We took important and opportune measures to evacuate people."

At 11 p.m. ET Thursday, Alex was pushing inland and had weakened to a tropical depression with sustained winds of 45 kilometres an hour, the U.S. National Hurricane Center said. It was expected to dissipate overnight.

However, the centre warned that the remnants of Alex are expected to produce additional rainfall of 75 to 150 millimetres in parts of northern Mexico and 50 to 100 millimetres in southern Texas, posing the risk of flash floods and mudslides.