The magnitude-seven quake was also felt strongly around 370km (230 miles) away in Mexico City, sending residents and tourists spilling into the streets from homes and hotels.
President Andrés Manuel López Obrador said there were no reports of major damage across the country.
Acapulco Mayor Adela Román said that the quake sparked “nervous breakdowns” in the city.
“People are worried because there are aftershocks.”
Many shaken residents slept in their cars and on the streets of the city as aftershocks continued, including one with a magnitude of 5.2.
An apparent light show flashed across the night sky during the tremors, with many posting videos to social media.
This rare phenomenon is known as earthquake lights (EQL). The US Geological Survey says that geophysicists differ in the extent to which they think that individual reports of unusual lighting associated with an earthquake actually represent EQL.
Some researchers think they occur due to friction between moving rocks creating electrical activity. Others say they are probably just lightning or electricity arcing between shaking power lines.
In Mexico City, many scared residents and tourists rushed into the streets in their pyjamas.
“It was terrible. It really reminds me of the 1985 quake every time something like this happens,” Yesmin Rizk, a 70-year-old resident, told the Reuters news agency.
A huge earthquake struck the Mexican capital in 1985, killing at least 10,000 people.
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