The arrest took place just days after the 39-year-old former world champion in middleweight lost his match against influencer Jake Paul in Anaheim, California.
According to lawyer Michael Goldstein, Chávez was arrested by a large number of federal agents when he was driving a moped outside his home.
The current charges are scandalous and just another trick to scare the public, says Goldstein according to AFP.
Chávez, who has previously been caught in drug tests and had problems with his weight during his career, is suspected in Mexico of arms and explosives smuggling as well as connections to the Sinaloa cartel. He also has an active arrest warrant.
The US immigration authorities state that Chávez exceeded his tourist visa, which expired in February, and that he was previously classified as a "serious threat to public safety". He is also alleged to have submitted false information in his application for a residence permit in April.
Chávez has had a turbulent career in the shadow of his legendary father and the world championship title from 2011 was the highlight. Before the meeting with Jake Paul, he claimed to be sober after drug rehabilitation.
