Mexico's disaster agency says it was an aftershock of the magnitude 8.1 quake that hit the state on 7 September, in which at least 90 people died.
The upscale Mexico City neighborhood was one of the hardest hit by the quake that killed at least 305 people, with more than a half-dozen collapsed buildings in the immediate vicinity.
The U.S. Geological Survey said the new, magnitude 6.1 temblor was centered about 11 miles (18 kilometers) south-southeast of Matias Romero in the state of Oaxaca, which was the region most battered by a magnitude 8.1 quake on September 7.
A 6.1 magnitude quake can produce strong shaking and considerable damage to poorly built structures and slight to moderate damage in better-constructed buildings, the USGS says.
Saturday's quake was centered in Oaxaca state near Matias Romero, a town about 275 miles southeast of Mexico City.
The tremor was mild in Mexico City but thousands of residents, many wearing pyjamas, ran into the streets when seismic alarms sounded.
There were no immediate reports of damage or casualties from the new quake, which was smaller and with its epicenter farther to the south than Tuesday's devastating 7.1-magnitude natural disaster that killed almost 300 people.
Initial reports from the Mexican Seismological authority said the quake struck at 07:53 am local time at a depth of 10 kilometers with an epicenter approximately 12 km north of the City of Ixtepec.
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Rescuers race against the clock early Saturday to reach possible survivors trapped inside an office building in the Roma Norte neighbourhood of Mexico City.
"Our first phase is rescue and humanitarian aid", Puente said. Schools closed indefinitely, and millions initially were without power.
He expressed hope that within three to four months, all the houses could be rebuilt and said that the aim was to make sure that the affected people could celebrate the New Year in a new house.
The government of Oaxaca state reported that some homes collapsed and one woman died when a wall of her home fell on her in the town of Asuncion Ixtaltepec.
"We had to hold on", he said.
Diana Pacheco texted her husband, told him where they were. "I want them to get out", Mr. Gutierrez said, his voice breaking.
"I was frightened because I thought: not again", she said.