The earthquake first struck just off the coast of Chile, about 144 miles north west of the capital Santiago, just before 8pm local time. Five people are known to have died, according to officials.
It caused waves of up to 4.5 metres (15ft) along the country's coastline, and this is now spreading to parts of California, Hawaii, Peru and even New Zealand.
The US' National Tsunami Warning Center has issued an alert for several miles along the western state's coast line, running from San Onofre in San Clemente - about 55 miles north of San Diego - to Ragged Point, which is about 50 miles north of San Luis Obispo.
The tsunami is expected to hit between 4:46am local time, travelling down to LA within one minute. It will then travel down to Santa Barbara by 5:06am and reach Port San Luis just four minutes later.
However weather forecasters are not predicting that the tsunami will be severe, and a "widespread inundation of land is not expected".
"No major destructive tsunami is expected; however, these areas are expected to see minor coastal flooding and strong or unusual currents, starting in the early morning on Thursday, " the US' National Weather Service said. "Tsunami waves could last several hours. Stay out of and away from the water."
Beaches along the affected parts of California are closed as of 4am local time.