Jesus Alfredo Guzman Salazar was arrested with another person in central Jalisco state in an operation by marines in the city of Zapopan.
His father is the boss of the powerful Sinaloa cartel.
"El Chapo", or "Shorty", Guzman has been in hiding ever since he escaped from prison in 2001.
Jesus Guzman and the other detainee, Kevin Beltran Rios, also accused of belonging to the Sinaloa cartel, were transferred to Mexico City, and paraded in front of the media.
A spokesman for the Mexican Navy, Jose Luis Vergara, said Jesus Guzman - known as "El Gordo", or "The Fat One" - was a growing force within the organisation.
Mr Vergara said Jesus Guzman also managed most of his fathers' properties. "El Chapo" Guzman appears on Forbes magazine's world billionaires list.
The BBC's Will Grant in Mexico City says the net could be tightening around El Chapo, with several of his close allies arrested recently.
Experts say the Mexican authorities seem to be trying to hurt Guzman by targeting his family.
The same tactic was employed by the Colombian army to get to the notorious drug baron Pablo Escobar.