Hermine has maximum sustained winds of about 65 mph (110 kph).
Hermine was moving north-northwest at about 14 mph (22 kph).
The storm was expected to bring as much as a foot of rainfall to some areas battered by Hurricane Alex in June.
Mexican authorities urged people to move to shelters while officials in Texas distributed sandbags and warned of flash floods as Tropical Storm Hermine strengthened and headed toward the northwestern Gulf coast.
Hermine "will briefly be over Mexico, and then we're expecting it to produce very heavy rainfall over south Texas," said Eric Blake, a hurricane specialist at the U.S. National Hurricane Center. "We're expecting widespread rainfall totals of 4 to 8 inches with isolated amounts of a foot possible. Especially in the hilly and mountainous terrain that could cause life-threatening flash flooding."
The storm's winds strengthened to about 60 mph (95 kph). Tropical storm force winds extended out up to 105 miles (165 kms) from the storm's center.
The cattle-ranching region is one the most dangerous in Mexico's turf war between two drug cartels. It is the same area 72 migrants were killed two weeks ago in what it believed to be Mexico's worst drug gang massacre to date.
Mexican emergency officials urged people living in low-lying coastal areas to move to shelters, but there were no immediate evacuation plans.
On the Texas coast, emergency officials readied pumping equipment and distributed sandbags in Cameron County, said John Cavazos, the county's emergency management coordinator. He said they are also suggesting that people in recreational vehicles in county parks along the coast should move.
He officials are worried about flooding because the ground is already saturated from earlier rains. Some areas could get up to 12 inches of rain, he said.
"Anyone living in ... an area that's known to flood, they need to take some precautions," Cavazos said.
Frank Torres, emergency management coordinator for Willacy County, said officials are preparing sandbags and making sure people know a storm is coming.
"It just popped up out of nowhere," he said. "We're anticipating some flooding. The good thing is it's going to blow through here very quickly."
No evacuations had been ordered in Texas.
In Hidalgo County, located inland, just west of Cameron and Willacy counties, officials were also distributing sandbags and anticipating the need to pump floodwaters
"Residents are urged to make preparations now and to remain alert to this rapidly-developing weather situation," Hidalgo County Judge Rene A. Ramirez said in a news release.