The quake struck at 0236 GMT Monday with an epicenter seven kilometers (four miles) north of Santa Monica and eight kilometers (five miles) northwest of Beverly Hills, reported the US Geological Survey, which monitors earthquakes worldwide.
Both towns are in the greater Los Angeles metropolitan area.
While most residents appeared to ignore Sunday’s tremor, on Friday a shallow 5.1-magnitude quake rocked the same region, causing power cuts, gas leaks and bursting water mains, and stopping rides at Disneyland.
The western US state is on the so-called Ring of Fire, which circles the Pacific and has produced a number of devastating quakes including Japan’s March 2011 quake-tsunami, which killed thousands of people.
Seismologists say a quake capable of causing widespread destruction is 99 percent certain to hit California in the next 30 years.