A woman, aged 50, died in the southwestern state of Guerrero when her home collapsed due to the tremors, the state's governor, Evelyn Salgado, said.
A 67-year-old man died while going down the stairs in Mexico City as he tried to evacuate his apartment building, local media reported.
Videos shared online showed the Angel of Independence - a golden angel atop a 45m-high column in a roundabout on one of the capital's busiest avenues - swaying from side to side as the earthquake hit.
The seismic alarm sent crowds evacuating into the streets, many wearing towels or pyjamas and cradling anxious pets.
The 6.5-magnitude quake struck near the Pacific Coast in the state of Guerrero at a depth of 35km, according to the US Geological Survey. The epicentre was about 289km away from the capital.
As of midday, Mexico's seismological service registered 420 aftershocks, the strongest of which was a magnitude 4.7.
Authorities reported landslides over highways, gas leaks, and damage to homes, public buildings and hospitals around Guerrero state. There were no immediate reports of people directly killed by the earthquake.
The southwestern state is home to Acapulco and other beach resort areas, which are a major draw for holiday tourists. Acapulco, the state's largest city, is still recovering from a Category 5 hurricane that devastated the area in 2023.
The earthquake also provided drama to Sheinbaum's daily press conference.
Sheinbaum was speaking at the National Palace in Mexico City when earthquake alarms sounded. She noted the ground was shaking beneath her before calmly evacuating alongside journalists. She resumed the press conference shortly afterward.
Mexico's aviation authority said the international airports of Mexico City and Acapulco had sustained some minor damage, but said those had not affected operations.
with AP
