When the quake struck at 11:49 p.m. local time, people fled to the streets in their pajamas. The massive 8.1 quake killed at least 61 people, authorities said.
Oaxaca Governor Alejandro Murat said that around three-dozen people in perished in Juchitan de Zaragoza, a city in the hard-hit Isthmus of Tehuantepec region, Efe news reported.
The state government says more than 1,000 homes were destroyed in Chiapas, and about 5,000 were damaged. At least 12 people have died as the storm has devastated the island nations of St. Martin, Barbuda, and the Turks and Caicos.
Chiapas and Oaxaca, home to about 9 million people, are two of the most impoverished areas in Mexico.
In a meeting with local and national neighbors and authorities, the president said that the force of nature can be devastating, but the unity and solidarity of Mexicans are much greater.
The death toll from Thursday's massive natural disaster off the coast of southern Mexico rose to 61 on Saturday as emergency responders scrambled to clear debris, restore power and provide housing for thousands of displaced people in one of the country's poorest and most remote regions.
The hurricane quickly lost strength after hitting land and was downgraded to a tropical storm.
In Veracruz, tourists abandoned coastal hotels as winds and rains picked up ahead of Hurricane Katia's expected landfall.
The Hurricane Center said Katia could still bring 3 to 6 inches (7.5 to 15 centimetres) of additional rain to a region with a history of deadly mudslides and flooding.
The country is observing three days of national mourning for the victims.
The Pacific Tsunami Warning Centre said tsunami waves had been detected but on Friday night United States time they confirmed that the "threat had now passed".
The National Hurricane Center says Katia has weakened into a tropical storm as it moves further into Mexico, with wind speeds of up to 45 miles per hour (72.4 kph). Lots of damage. Lots of deaths. To the east, Hurricane Jose, a Category 4 storm, was following behind, threatening further damage in Irma's wake. A third of the homes in Juchitan, Oaxaca, were also toppled or rendered uninhabitable.
In downtown Juchitan, the remains of brick walls and clay tile roofs cluttered streets as families dragged mattresses onto sidewalks to spend a second anxious night sleeping outdoors.
A magnitude 8.2 quake off the coast of Mexico is one of the most powerful ever recorded in the Central American country. Some of the people were newly homeless, while others feared that aftershocks could topple their cracked adobe dwellings.
He said the possible death occurred in San Marcos state near the border with Mexico.