US customs officials say Jose Aguilar was arrested by federal agents who found four illegal migrants from China in the boot of his car.
The lawyer representing Mr Aguilar, Jeremy Warren, said the case had nothing to do with the famous singer.
"Jose Aguilar is a young man who will address this matter in court, not with the press," he said.
The arrest took place two weeks ago - but details, including Jose Aguilar's involvement, emerged on Friday.
US Customs and Border Protection said Mr Aguilar was arrested at the border in San Diego after a sniffer dog alerted federal agents to the stowaways in the boot of his car.
The migrants reportedly said they had agreed to pay Mr Aguilar between $3,000 and $60,000 (Â£2,390 and Â£47,830) to be smuggled into the US.
Mr Aguilar, who is a US citizen, was released on bail pending his arraignment.
His father, Pepe Aguilar, is one of Mexico's most popular mariachi singers.
He has won four Grammy awards and four Latin Grammy awards and has a star on the Hollywood Walk of Fame.
The son of the popular Mexican singer Pepe Aguilar has been arrested in California for people smuggling.