Schwarzenegger told reporters about the threats against Mayor Antonio Villaraigosa and Lt. Gov. Cruz Bustamante during a news conference in his office Monday.
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.
Congress is returning from a two-week break and still faces long odds in passing any immigration bill at all, reports CBS News correspondent Bob Fuss. The House passed a bill that sparked protests around the nation; it would make all illegal immigrants into felons and also seek to jail anyone who helps them.
The Senate came close to passing a bill the president likes to let most of the 12 million illegal immigrants become legal. But with opposition from many Republicans and political maneuvering on both sides, efforts to pass it collapsed and it won't be easy to get back on track.
Bustamante and Villaraigosa have opposed the criminalization of illegal immigrants and have said they support legal pathways to helping undocumented workers become citizens.
Schwarzenegger also said he is 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."
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.