The large tremor also triggered alarm 680 kilometers (422 miles) away in Mexico City, where rescue and recovery efforts are continuing following Tuesday's 7.1-magnitude natural disaster.
Although Oaxaca State is located in Southern Mexico, Saturday's quake could be felt almost 300 miles away in Mexico City.
There were no immediate reports of major new damage or casualties in the Mexican capital, but there appeared to be some in Oaxaca, including a downed bridge and further damage to homes and other structures already tottering since the earlier quake.
Mexican President Enrique Pena Nieto, who declared three days of national mourning, has said saving lives is the top priority.
After the 7.1 magnitude natural disaster rocked Mexico City on Tuesday killing over 250 people and leaving hundreds of homes, buildings and structures in uninhabitable conditions.
Magnitude 6.1 natural disaster strikes southern Mexico, swaying buildings in Mexico City
At 8:24 a.m. there was another magnitude 5.2 quake, located to the northeast of Ciudad Ixtepec. According to Save the Children's Hanna Monsivais, hundreds have flooded into the streets to help with rescue efforts after the quake. The aftershock swayed buildings and prompted civil defense officials to temporarily suspend rescue operations in the rubble of buildings downed by Thursday's quake.
Frida has spent most of her efforts at a school in southern Mexico City where 19 school children and six adults died, but 11 more children were rescued.
Power was restored to 4.63 million households and business on the night of September 21, representing 95% of those that had lost power after the quake, according to the Federal Electricity Commission, AIR said. The buildings that collapsed were mostly constructed aeons ago.
"Bulldozers and other equipment may drown out the sound of thunder, so crews should pay extra attention to weather conditions and be prepared to seek shelter indoors for a time", she said. "Until we are absolutely certain that there are no more people missing, we will continue our search and rescue mission", he said.
On Friday, an quake measuring 5.8 on the Richter scale has struck off California in the Pacific Ocean, the US Geological Survey (USGS) said.