At least eight people were killed and 16 wounded, the authorities say, with vehicles left burning in the streets.
President Andres Manuel Lopez Obrador said the decision to cancel the arrest on Thursday had saved lives.
Senior security officials had decided on his release, the president said at a news conference. "The officials who took this decision did well," he said.
"The capture of a criminal is not worth more than people's lives."
lawyer for the Guzmán family appeared before journalists and described the president as "human" and "Christian". He had decided "not to cause Ovidio harm", Jose Luis Gonzalez Meza said.
There was no negotiation to free him, he added.