It marked the second powerful quake to hit Mexico in less than two weeks, after an 8.1 magnitude natural disaster struck off the country's Pacific coast 12 days earlier.
No one knows for certain how many pets are missing but many of Mexico City's hardest-hit areas are filled with dog-friendly restaurants, parks and upscale groomers.
There were no reports of new damage in the capital and rescue efforts were still the priority, Mexico City's Mayor Miguel Ángel Mancera said on Twitter (in Spanish).
No new damage was immediately reported but rescue efforts were suspended to allow authorities to see if the new tremors would put workers at risk, said Luis Felipe Puente, the head of Mexico's civil protection agency.
Meanwhile, the bodies of eight foreigners have been recovered from the rubble of the quake that struck Mexico City, officials have said.
Much of the national & global attention in recent days was focused on at the Enrique Rebsamen school, where at least 25 people - including 19 children - died.
The quake, with a magnitude of 5.8, was then followed by a second quake of 5.6 closer to shore, The Sun reported.
However it sparked concern that it could have caused heavy rubble on top of survivors awaiting rescue in Mexico City to shift. Altogether, earthquakes have killed at least 380 people in September.
Many buildings had toppled in Mexico city- the capital of Mexico.
Buildings swayed in Mexico City, where nerves are still raw from Tuesday's magnitude 7.1 temblor that has killed over 300 across the region. The United States Geological Survey has stated that quake of magnitude 6.1 is powerful enough to damage poorly built building. The buildings that collapsed were mostly constructed aeons ago.
Mexico's Navy said Friday that 115 people have been found alive by rescuers in Mexico City.
"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.