The photos, posted by Mexican website Blog del Narco, show a man, purportedly Jesus Alfredo Guzman Salazar, 29, son of El Chapo on his knees with his hands behind his head as a man points a gun at him.
Other pictures show several people sitting at a table inside the restaurant before the kidnapping occurred. When the rival cartel members entered the restaurant, numerous diners are held at gunpoint as they stand by the table.
A squad of seven armed gunmen, believed to be from Jalisco New Generation cartel, took the men hostage at 1am on Monday.
Joaquin Guzman, who famously escaped from a maximum security prison through a mile long tunnel from under his cell, is the head of the rival Sinaloa cartel. After his recapture in January, his sons took over control of the gang, the biggest and once most feared of the Mexican gangs.