Other elected officials of Mexican heritage have also received threats, Schwarzenegger said, but he did not name them.
Bustamante spokesman Steve Green said the lieutenant governor appeared at some immigration rallies with Villaraigosa in March and received "nasty e-mails" afterward. The death threat — "The only good Mexican is a dead Mexican" — came about three weeks ago on a postcard, he said.
The California Highway Patrol, which investigates threats against public officials, declined to comment.
Janelle Erickson, a spokeswoman for Villaraigosa, said she didn't know whether the mayor had received threats related to the immigration debate.
Bustamante and Villaraigosa have opposed the criminalization of illegal immigrants and have said they support legal pathways to helping undocumented workers become citizens.
Schwarzenegger said he also was disturbed that vandals had spray-painted ethnic insults on and torched a Mexican-owned restaurant in San Diego County this month. Officials ruled the April 10 attack a hate crime.
"That is not what California stands for," Schwarzenegger said. "I've asked the district attorneys throughout our state to be vigilant and swift in their actions against those who practice hate against our fellow citizens."
Schwarzenegger's comments came the same day that President Bush addressed illegal immigration during a speech in Orange County, near Los Angeles.
The governor has said he opposes amnesty for illegal immigrants, but he also called a massive deportation of the estimated 11 million foreigners living illegally in the U.S. unrealistic.
Bush gave the same message Monday.