Thirteen others were left seriously injured following the blaze in the southern port city of Coatzacoalcos, NBC said, citing a statement from the state attorney general's office.
The office condemned "what may constitute a malicious attack," it added.
Fire erupts in medical college warehouse
Citing reports, The Los Angeles Times said Molotov cocktails had been thrown into the bar.
Images carried by local media showed a wrecked interior with chairs overturned and debris littering the floor, and emergency vehicles and police outside the building.
"The devious crime of a few moments ago in Coatzacoalcos will not go unpunished," the governor of Veracruz state said in a tweet.
Veracruz is one of the most violent regions of Mexico. Drug trafficking routes to the United States pass through it, and bloody battles frequently erupt between rival drug gangs.
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