A massive manhunt was launched after Guzman vanished late Saturday from the Altiplano maximum-security prison, some 90 kilometers west of Mexico City.
The Sinaloa cartel kingpin, whose empire stretches around the globe, had been in prison for 17 months, since his recapture in February 2014.
After security cameras lost sight of Guzman, guards went into the cell and found a hole 10 metres (33 feet) deep with a ladder, National Security Commissioner Monte Alejandro Rubido said.
A motorcycle on a rail system was found in the tunnel and is believed to have been used to transport tools and remove earth from the space, which was 1.7 metres high and around 80 centimetres wide.
Rubido said 18 prison guards were sent to Mexico City to be interrogated by prosecutors, signalling suspicion of a possible inside job.
Until Guzman escaped, Rubido said, "the day had gone on normally and at around 8:00 pm he was given his daily dose of medicine."
Soldiers manned checkpoints on the nearby highway, searching car trunks and the backs of trucks.
Flights were suspended at the nearby Toluca airport.
The Altiplano prison in central Mexico State houses the country's most notorious drug lords, murderers and kidnappers.
Guzman's first break from prison was in 2001, when he slipped past authorities by hiding in a laundry cart. He had been arrested in Guatemala in 1993 and that country's troops were put on alert at the border today.
Marines had recaptured him in February 2014 in a pre-dawn raid in a condo in Mazatlan, a Pacific resort in Sinaloa state, with the help of the US Drug Enforcement Administration.
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