Another 11 were badly injured in the blaze in the Caballo Blanco (White Horse) bar in Coatzacoalcos, a port city in Veracruz, on Tuesday night.
Survivors said men believed to be gangsters blocked the exits before setting the venue on fire.
Mexican media reported that the bar was peppered with gunfire and Molotov cocktails were thrown inside.
President Andrés Manuel López Obrador said the attack was "shameful", and that an investigation would look into how some of the suspects had recently been freed from custody.
