The drug capos were arrested after a raid by Mexican soldiers on a house in the Lomas Altas neighborhood in Zapopan around midday Friday.
Several bursts of gunfire were exchanged during the operation in the Guadalajara metro area suburb.
Valencia, also known by his alias "El 85," was a former member of the Milenio Cartel, and closely allied with Sinaloa Cartel leader Ignacio "Nacho" Coronel, who died in Guadalajara in 2010 in another military operation.
Valencia formed the Jalisco Nueva Generacion Cartel in the wake of Coronel's death.
In the hours following the arrests, gangs of armed men, presumably working for the Jalisco Nueva Generacion Cartel, commandeered buses and other vehicles in Guadalajara and other parts of the state, setting many of them on fire. The disturbances mobilized hundreds of security and emergency personnel and created significant panic, as well as traffic jams.
A Defense Department spokesperson suggested the disturbances were orchestrated to distract security forces from taking further action against the drug cartel.