The bill was discussed on the Assembly floor for 7 minutes before being approved last week on a 48-to-28 vote, the Los Angeles Times reported Wednesday.
Democrat Assemblyman Bob Wieckowski, chairman of the Judiciary Committee that sponsored the bill, said the measure's goal was to make jury pools more inclusive.
"Immigrants are our friends, immigrants are our neighbors, immigrants are our co-workers, immigrants are our family members," Wieckowski said.
He said there were 3.4 million permanent, non-citizen immigrants in California who aren't included in jury pools, the Times said.
"We lose their perspectives," the lawmaker said.
But Rocky Chavez, a Republican, said some people migrated from countries where suspects are presumed to be guilty until proven innocent.
"We actually are taught to question authority," Chavez said. "Some cultures are taught to obey authority."
Jury peers, he said, "are people who understand the nuances of America," he said during floor debate.
The Times said there was no indication on what action Brown would take on the bill.