The El Paso Fire Department on Friday reported nobody was hurt in the blaze that destroyed the structure.
Authorities are trying to determine what started the fire Thursday night at what was known as the John Wesley Hardin Building.
A 1962 historic marker described Hardin as "the West's most feared gunman" who killed at least 26 men. The marker says Hardin was shot dead at the Acme Saloon in El Paso on Aug. 19, 1895.
El Paso City Council member Steve Ortega says the Hardin structure was one of the most historic buildings in El Paso.
No damage estimate was immediately released.