At least 13 people were killed, including three children, Acuña Mayor Evaristo Lenin Perez said. Another 200 were injured.
Photos from the scene, which sits right across the border from Del Rio, Texas, showed cars blown upright, front bumper on the ground and leaning against homes. The twister flipped over school buses and damaged about 400 homes.
Officials said records don't show such a powerful tornado hitting the city in more than a century.
The storm system that spawned the deadly tornado is the same one whose rains have caused flooding in Central Texas.
Monday's thunderstorm dumped rain and hail on both communities straddling the border, but it was Acuña that bore brunt of the severe weather.
The part of Acuña where the tornado struck is densely populated, making the damage all that more severe.
One resident, walking around the damaged area, said he saw part of a car that had been tossed to the summit of a hill.
"You can also see another truck that was flung by the wind into the side of the hill," Homero Iracheta said.
Neighbors from across the international bridge in Del Rio
Acuña is a historic border city that people outside of Mexico know as the setting for Robert Rodriguez's films "El Mariachi" and "Desperado," and George Strait's song, "Blame it on Mexico."
Mexican President Enrique Peña Nieto announced that he will visit Acuña, about 155 miles west of San Antonio, Texas, to survey the damage.