On Thursday officials paraded before the media a man they said was Jesus Alfredo Guzman, whose father leads the powerful Sinaloa cartel.
But the arrested man was in fact Felix Beltran Leon, a car salesman, the attorney general's office said.
The authorities had hailed the arrest as the most important in years.
Known as El Chapo" or "Shorty", Joaquin Guzman has been in hiding ever since he escaped from prison in 2001.
The Sinaloa cartel controls much of the flow of cocaine, marijuana and methamphetamine to the United States.
The BBC's Will Grant in the capital, Mexico City, says within hours of the high-profile arrest, doubts had started to be cast on the official version of events.
A lawyer proclaiming to speak for the Guzman family released a statement denying that the suspect in custody was the drug boss's son.
Mr Beltran Leon's mother then spoke to journalists and denied any link to Joaquin Guzman or the Sinaloa cartel.
It took another few hours, while identity tests were carried out, before the government admitted it had made a huge mistake.
In less than a day, the episode has transformed from an apparent coup against one of Mexico's biggest drug cartels to a major embarrassment for President Felipe Calderon's administration, our reporter says.
US agencies, such as the Drug Enforcement Administration, were among those that had applauded the arrest.