The protesters skirmished with police along several streets in the Crenshaw District in southwestern Los Angeles.
Businesses including a Wal-Mart store were damaged as some 150 people "sought to exploit" Zimmerman being cleared of murdering black teenager Trayvon Martin, LA mayor Eric Garcetti said.
"We should respect Martin family's call for peace. Unlawful assembly declared. Police are clearing area," he said on Twitter after unrest erupted following an early evening prayer rally.
The protesters skirmished with police along several streets in the Crenshaw District in southwestern Los Angeles.
The Wal-Mart store was damaged, and a restaurant window smashed, local media reported.
Some demonstrators stomped on cars, assaulted bystanders and vandalised property, according to the Los Angeles Times.
Chunks of concrete were hurled at officers at one point, the newspaper reported, citing authorities.
At least 13 arrests were made, Garcetti said.
'Violence is never the answer'
The Martin case pitted people who thought Zimmerman (29) – son of a white father and a Peruvian mother – killed Martin (17) in self-defense in Sanford, Florida last February, against others who considered it a racially-motivated killing.
Los Angeles police department chief Charlie Beck tweeted: "Violence is never the answer. Urging all protesters around LA 2 let peace prevail. This is OUR City and we need to work 2gether 2 preserve it."
The incidents followed protests Sunday night including one in which riot police broke up an 'unlawful assembly" outside the CNN building in Hollywood, arresting at least six people.
Meanwhile multiple arrests were made further north in Oakland, on the San Francisco Bay, after hundreds of protesters stormed an interstate road and blocked traffic, the LA Times reported.
Los Angeles is ever mindful of the deadly April 1992 riots in the city, which broke out after a similar racially-tinged trial.
Several protests erupted across the United States following Saturday's acquittal of Zimmerman. – AFP