The first tremor struck Sunday evening just after 8:30 p.m. local time from an epicenter about 10 miles (16 km) southwest of the Los Angeles Civic Center.
The quake damaged walls in a Long Beach apartment building, where 18 residents had to evacuate due to fears that the structure might collapse.
The shaking was felt widely across Southern California for around 15 seconds due to a slip of the Newport-Inglewood fault, which seismologists have long feared could produce a devastating earthquake.
Stretching 50 miles (80 km) across the Los Angeles Basin, the fault was responsible for the damaging 1933 Long Beach earthquake. It is believed capable of generating a catastrophic quake of around magnitude 7.
The second tremor registered a magnitude of 4.1 when it struck on Tuesday afternoon at 3:49 p.m. near the same epicenter.
The last significant seismic event to strike Los Angeles came last July when a magnitude 5.4 temblor became the most powerful jolt to hit the city in 14 years.