US authorities were outraged by the surprise release of Caro Quintero, who had served just 28 years of a 40-year sentence for the abduction, torture and killing of a US drug agent in 1985.
The 60-year-old, once a senior figure in a now-defunct cartel, was convicted of killing the US Drug Enforcement Agency's Enrique Camarena and his Mexican pilot Alfredo Zavala.
But on August 7 a judge in the western state of Jalisco ordered his release, and Caro Quintero has gone missing since he left prison.
If and when Caro Quintero is detained, US authorities will have 60 days to submit a formal extradition request, it added.
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The US National Security Council had said Sunday it was "deeply concerned" by Caro Quintero's release and feared another individual connected to the Camarena killing could also be set free.
Mexican Foreign Minister Jose Antonio Meade downplayed the dispute over the release, saying it would not affect relations with Washington because both governments opposed the court ruling, which he said should be "revised."