Across the border in the United States, flooding has affected the state of Texas.
Authorities in Mexico say the tornado reached a speed of up to 186 miles an hour.
At least fifteen people have died as a result of the disasters.
Evaristo Lenin Perez, Mayor of Ciudad Acuna, said it was the first tornado to hit the city since it was founded more than 100 years ago.
Rescuers are searching the damaged homes for survivors.
"There are cars on top of houses... it is total chaos," local resident Maria del Rosario Ramirez told Mexican newspaper La Jornada.
BBC reporter Katy Watsons said: "The tornado only lasted a short moment but that was enough to devastate a community."
"It struck at a busy time in the morning - people were driving or taking public transport to work."
"The army is helping to search for missing people and neighbouring states have also said they will lend a hand in the rescue effort," she said.
A deadly tornado has hit Mexico, with hundreds of homes damaged or destroyed in the city of Ciudad Acuna.