Carrillo Leyva is the son of Amado Carrillo Fuentes, who was one of Mexico's leading drug traffickers before he died during plastic surgery to change his appearance in 1997.
Fuentes was nicknamed "the Lord of the Skies" because of his success in sending aircraft full of cocaine to the US.
After his death, Fuentes's brother Vicente took over the cartel while Carrillo Leyva became second-in-command, the Mexican attorney-general's office said.
The office had put Carrillo Leyva on a list of 24 of the country's most-wanted drug suspects and offered a reward of 30 million pesos ($2.1 million) for his capture.
The same amount was offered for the capture of Vicente.
The Juarez cartel, which operates in the city of Ciudad Juarez on the US border, is one of the major drug gangs involved in bloody battles over lucrative trafficking routes into the US.
More than 1,000 people have been killed so far this year alone in suspected drug attacks, and about 6,000 died in spiraling violence last year.