He moved up after the arrest of his brother, Francisco Javier Arellano Felix, according to Facundo Rosas, the deputy secretary of Mexico's police intelligence.
Al Jazeera's Franc Contreras said the arrest was a major blow to the cartel thought to be very heavily armed and very powerful.
"Investigators here tell us that perhaps this organisation is more heavily armed than the Mexican army and federal police force themselves," Contreras said, reporting from Mexico City.
But analysts warn that the arrest will not necessarily dismantle the trafficking organisation.
"Those people watching the drugs trade say that at any moment another member of the family, or another cartel, could swoop in and recover control," he said.
Arellano Felix was located in a house in the border area of Tijuana, and fired on federal agents after being encircled, police said.
A three-hour gun battle with more than 100 police and soldiers ensued before his arrest.
He was found with a girl, aged 11, believed to be his daughter, police said.
His drug cartel, also known as the Tijuana cartel, is allegedly one of the four large drug mafias operating in Mexico and is blamed by the US justice department for importing and distributing hundreds of tonnes of cocaine and marijuana in the US.
It has also been blamed for the murder and torture of police officers, informants and rivals.