Jesus Alfredo Guzman, 29, was one of six members of the Sinaloa Cartel seized by members of a rival gang, Jalisco New Generation.
The incident took place at a restaurant in the resort city.
Joaquin “El Chapo” Guzman, who is in jail, led the Sinaloa Cartel for years. Jesus Alfredo Guzman is suspected to be a senior member.
He is wanted on drugs charges by the US.
The US also wants El Chapo Guzman to be extradited on charges of smuggling vast amounts of drugs into the country.
The drug lord was recaptured in January, six months after escaping through a one-mile tunnel from his maximum-security prison cell.
The six suspected gang members were abducted at La Leche restaurant in the early hours of Monday in Puerto Vallarta, Jalisco state.
State Attorney General Eduardo Almaguer told reporters that forensic evidence collected at the scene had confirmed Jesus Alfredo Guzman’s abduction.
He added that four of the six kidnapped people had already been identified, without providing further details.
There are reports that another of El Chapo Guzman’s sons, Ivan, may have also been among the victims.
Local officials say the victims had traveled from neighboring states for a celebration in the upscale restaurant.
Jalisco New Generation and the Sinaloa Cartel have been fighting for the control of major drug routes along Mexico’s Pacific coast.
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