Scores of homes have been destroyed in the city, in Coahuila state, which is just across the border from  Del Rio, Texas.
Images from the scene showed cars upended and leaning against buildings.
Local media said the death toll could rise as more destroyed homes were searched.
Rosario Cano, a spokeswoman for Coahuila's interior department, said the tornado had struck at about 06:40 (11:40 GMT).
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At least seven people are reported to have been killed by a tornado that hit the northern Mexico border city of Ciudad Acuna.