The attorney general's office said in a statement that Interpol Mexico agents went to Guzman's prison near Mexico City to execute two arrest warrants, launching the proceedings.
Judges will now have to issue a ruling and handed it over to the foreign ministry, which has to give the green light to any extradition.
"It must be noted that the defendant has the possibility of seeking an injunction against the decisions issued by the foreign ministry," the statement said.
The extradition bid marks a reversal from President Enrique Pena Nieto's refusal to send Guzman across the border prior to his July escape from a maximum-security prison.
Mexico received two US extradition requests last year on a slew of charges, including drug trafficking and homicide. Guzman is wanted in a half-dozen US states.
His attorney has vowed to challenge the extradition.
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