They say 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 of Puerto Vallarta .
Guzman, who is now in jail, had led the Sinaloa Cartel for years. Jesus Alfredo is suspected to be a senior member.
The 29-year-old is wanted on drugs charges by the US.
The US also wants Joaquin "El Chapo" Guzman to be extradited to the US on charges of smuggling vast amounts of drugs into the country.
He was recaptured in January, six months after escaping through a 1.6km (one-mile) tunnel from his maximum-security prison cell.
Cartel war warning
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 Guzman's son, Ivan, may have also been among the victims.
Local officials say the victims had travelled from neighbouring states for a celebration in the upscale restaurant.
The BBC's Juan Paullier in Mexico says the kidnap may trigger a war between the two major Mexican drug cartels.
Jalisco New Generation and the Sinaloa Cartel have been fighting for the control of major drug routes along Mexico's Pacific coast.
Mexican gangs smuggle tonnes of illegal drugs - mainly cocaine - to the US every year.