A special unit "detained the attacker of the consular official," the Jalisco state prosecutor's office said on Twitter.
The suspect was handed over to the federal attorney general's office, the state authorities said, without providing details about the arrest or a possible motive for the attack.
The FBI had offered $20,000 for information about the shooter's identity.
The unidentified consular official was driving out of a shopping center's garage on Friday evening when a man wearing a black wig and a blue nurse uniform, who had been waiting outside, fired at the car, according to surveillance camera footage.
Guadalajara and the rest of the state have been hit by violence perpetrated by the powerful Jalisco New Generation drug cartel in recent years.