They interrupted a group of revelers in the white-walled restaurant, separating the men from the women, and left with a high-value captive, according to Mexican authorities.
Jesus Alfredo Guzman, the 29-year-old son of jailed Mexican drug lord Joaquin "El Chapo" Guzman, was among the six men kidnapped, Jalisco Attorney General Eduardo Almaguer said at a news conference Tuesday.
The kidnapping is the latest blow to the elder Guzman's efforts from behind bars to maintain Sinaloa cartel's dominance in the region amid challenges from an emerging rival, the Jalisco New Generation cartel.
Jesus Alfredo and his brother Ivan Archivaldo Guzman are thought to be involved with the Sinaloa cartel, along with Guzman's son by another woman, Ovidio Guzmán Lopez.
Though Almaguer did not attribute the kidnappings to New Generation, he said that a criminal group was responsible.
Witness interviews, surveillance video and a search of five vehicles parked outside La Leche led to the identification of Jesus Alfredo and three other men, all with ties to organized crime, Almaguer said. The additional men men were identified as Juan Daniel Calva Tapia, 53, Josias Nahujali Rabago Borbolla, 35 and Víctor Galvan Ureña, 46.
"At this moment, we have identified four of the kidnapped," Almaguer said, "one of them being Jesus Alfredo Guzman."
The Mexican army, marines, federal police, state police and the country's top prosecution office are searching for the missing men as well as those responsible, Almaguer said.
No one has contacted Mexican authorities to report the men missing, and authorities have not heard from the kidnappers, Almaguer said.
Jesus Alfredo is the youngest of El Chapo's two children from his first marriage. His older brother, Ivan Archivaldo Guzman, was imprisoned in Mexico in 2005, but released three years later for lack of evidence.
Earlier Tuesday, Guzman family attorney Pablo Badillo said it was "very likely" that Ivan Archivaldo was abducted from the restaurant. Badillo told CNN the Guzman family contacted him Tuesday afternoon and told him that "the possibility of Ivan Archivaldo having been abducted is very high."
Almaguer had also said that Ivan Archivaldo was among those kidnapped, though he eventually backpedaled on the claim.
Ivan Archivaldo's name did not come up at Tuesday night's news conference, and it was not immediately clear whether he was among those kidnapped.