Guzman, Mexico's most wanted criminal and boss of the feared Sinaloa Cartel, was caught in the northwest of the country with help from U.S. agents in a pre-dawn raid on Saturday.
The dramatic capture ended his reign as one of the world's most notorious organized crime bosses, and was a major victory for the Mexican government in a long, brutal war.
According to a Mexican justice official, Guzman's lawyers filed the injunction on Monday after the spokesman for a U.S. federal prosecutor said he planned to seek the capo's extradition to face trial in the United States.
However, it is still unclear whether that will happen, and extradition proceedings can take years to complete.
Earlier on Monday, a U.S. Justice Department spokesman said an extradition decision would "be the subject of further discussion between the United States and Mexico". U.S. officials said that President Barack Obama's administration wanted to avoid looking like it was putting pressure on Mexico to move quickly on an extradition.
Mexico has not yet said whether it is ready to do so.
"The security cabinet will need to meet and take the most appropriate decision," Interior Minister Miguel Angel Osorio Chong told a radio station on Monday.
Sensitivities over the issue could mean Guzman is more likely to face justice first in Mexico, where he still has an outstanding term to finish after he broke out of prison in 2001.
Fears of a repeat escape might encourage Mexico's government to hand Guzman over to the United States, but it would also be a tacit admission of ongoing weakness in the justice system. Crime bosses have served terms first in one country, then the other.
While Guzman has been charged with an array of crimes in Mexico, murder is not among them, government and justice officials said. That is despite accusations by security officials that his cartel was behind thousands of killings.
"The main charges against him are for organized crime, drug trafficking, arms trafficking," said an official at the attorney general's office, adding there were six arrest orders for Guzman. "There were no murder charges ... in any of the arrest orders," the official added. The charges could carry a combined total sentence of up to 400 years, the officials said.
The 56-year-old kingpin is being held in the Altiplano prison in the State of Mexico, outside the capital. He gave a brief statement to a judge on Sunday, and is being kept in a cell alone in a maximum security area.
More than 80,000 people have been killed in Mexico's cartel violence over the last seven years with much of the killing in western and northern regions at the heart of smuggling routes.
The United States had a $5 million bounty on Guzman's head. His cartel has smuggled billions of dollars' worth of cocaine, marijuana and methamphetamine into the United States, and fought brutal turf wars with other gangs across Mexico.
In addition to facing U.S. criminal charges in Chicago and New York, Guzman was indicted in 2007 in Miami for cocaine smuggling, with additional charges added last month.
He was also charged in Texas with importing cocaine and marijuana, money laundering, firearms violations and running a criminal enterprise that included murder.