Some 300 houses were damaged by the twister in Ciudad Acuna, the mayor said.
A seven-year-old boy is missing, mayor Lenin Perez said in a tweet.
The tornado was so powerful that big rig trucks were sent flying into the air and landed on houses.
Firefighters and civil protection officials rushed to the town to start searching for survivors among the rubble of ruined buildings.
The tornado lasted just a few seconds in the city of 136,000. Most of the fatalities were people who were out on the street, the mayor said.
Telephone service to the city has been partially disrupted.