His relatives claim it is punishment for his high-profile escape from the same jail in July 2014
Joaquin "El Chapo" Guzman has claimed returning to a maximum-security prison following his recapture is turning him into a "zombie", as he is being treated inhumanely by the authorities.
The Mexican drug lord is alleging that guards are waking him up in the middle of the night, and are failing to give him enough clothes to stay warm in his cold cell.
His relatives, who claim the "torture" is punishment for his high-profile escape from the same jail in July 2014, have staged a protest outside the small compound.
Bernarda, his sister, said: "They are angry because he got out, but anybody, even an irrational animal, would seek their freedom. He didn't hurt anybody."
Earlier in the week, one of Guzman's lawyers, Jose Refugio Rodriguez, told reporters that his client hated life inside the Mexican jail so much that he is now eager to be extradited to the US.
In order to speed up the process, the head of the Sinaloa cartel is even willing to plead guilty to any charges - as long as authorities provide him with a short sentence in a medium-security prison.
"I saw a desperate man, a dejected man," Mr Rodriguez said. "I found him very discouraged and in a very serious state of health."
Another member of El Chapo's legal team, Juan Luis Gonzalez Meza, said he planned to go on "hunger strike" until the 58-year-old began receiving better treatment.
However, the lawyer later admitted he would still be having breakfast and juice every day.
Mexican authorities have denied that Guzman is being treated inhumanely, and insist that he is in good health.
The protest came as the kingpin's eldest daughter, Rosa, told The Guardian that her father had managed to sneak into the US twice during his stint as a fugitive.
Although she refused to reveal how he had managed to cross the border, she claimed that his dramatic jailbreak through a tunnel was not an escape, but an "agreement" with senior officials.
More than 30 people, including the warden of the prison he escaped from, were arrested after his disappearance.