Ovidio Guzmán Lopez was reportedly arrested in the western city of Culiacán, the stronghold of the powerful Sinaloa drug cartel. His capture had triggered heavy gun battles between suspected cartel members and the security forces across the city, the BBC reported.
The statement from the local police, however, was doubted by Mexican security secretary Alfonso Durazo who said 30 members of the National Guard and army were patrolling in Culiacan when they were fired on from a house. They repelled the attack and inside the house found Ovidio Guzman Lopez.
Durazo said the house was then surrounded by heavily armed gunmen who had "a greater force" and authorities decided to suspend the operation. He did not say if Ovidio Guzman was arrested or went free after being located.
Later, Mexican Security Minister Alfonso Durazo told Reuters that the security forces released the drug lord's son from a house where they apprehended him. The decision was made to protect lives, the minister said.
Ovidio Guzmán, said to be in his 20s, is believed to have played a key role in the Sinaloa cartel following the arrest of his father, Joaquín "El Chapo" Guzmán, who was sentenced to life in prison plus 30 years in the US back in July.
Lopez is wanted in the US on several drug-related charges, Mexican media report.
The Sinaloa state government said it was "working to restore calm and order in the face of the high-impact incidents that have occurred in recent hours in various points around Culiacán", AFP news agency reports.
Mexican President Andrés Manuel López Obrador said he would make a statement later on Thursday.
El Chapo (or "Shorty") ran the Sinaloa cartel across northern Mexico, becoming one of the biggest traffickers of drugs to the US. In 2009, Guzmán entered Forbes' list of the world's richest men at number 701, with an estimated worth of $1bn. He was accused of having helped export hundreds of tonnes of cocaine into the US and of conspiring to manufacture and distribute heroin, methamphetamine and marijuana. He is also known for his escape attempts, breaking from Mexican jail through a tunnel in 2015. He was later arrested and extradited to the United States in 2017.