A judge granted him "provisional suspension", meaning that the foreign ministry has 48 hours to present a report justifying its decision.
The Mexican drug boss will file multiple legal challenges against Friday's ruling to extradite him to the U.S.
He is currently held in a prison in Ciudad Juárez.
His extradition to face murder charges in Texas can proceed.
Guzmán Loera's lawyer said that it is not the same as having the process actually starting.
Cleofas Alberto was arrested on March 13 in Mexico City.
The U.S. has a 60-day window to request the extradition of Brenda Berenice Delgado Reynaga.
Guzmán asked his lawyer to negotiate with U.S. authorities for a lighter sentence and confinement at a medium-security prison.
Peña Nieto accepted that the last escape of the drug lord represented a tense moment to his government.
Guzmán's extradition to face charges in the United States was discussed on Tuesday at a meeting in Miami between Arely Gómez, Mexico's attorney general, and Justice officials.