"As of now, the information is uncorroborated and the credibility of the source is unknown," the LAPD said in a statement.
No specific shopping mall was named, but the warning indicated a mall near the Federal Building in West Los Angeles could be targeted.
The LAPD will increase patrols at shopping malls in the city and asked mall operators to beef up security while a joint terrorism task force investigates. The department said it would have no further comment beyond the statement issued late Wednesday.
Mayor James Hahn's spokeswoman Shannon Murphy said that while the threat was uncorroborated, the city was "asking all Los Angeles residents to go on with their daily lives while remaining vigilant and alert."
The Los Angeles Times reports the threat came in an anonymous phone call to federal homeland security officials.
"This just happens all the time," The Times quoted Gene Thompson, the security chief for a firm that owns two area malls, as saying. "We take these things very seriously. This is no different than any anonymous bomb threat that gets called in all the time."
Since Sept. 11, U.S. authorities have tracked a multitude of threats to targets as diverse as fuel tanker trucks, the Brooklyn Bridge, apartment buildings and Gulf Cost petrochemical facilities.
In February, the Utah Capitol was evacuated and armed police with bomb-sniffing dogs searched the building after a "credible" bomb threat was made. A day earlier, one of the U.S.-Canada border's busiest crossings was closed for about an hour after guards found a grenade in the glove compartment of a car leaving the United States.
A Delta Airlines jet traveling from Germany to the United States made an emergency landing in Ireland in January because of a bomb threat.