Rescue workers are searching for survivors buried under rubble and officials warn the death toll may rise.
The 7.1 magnitude quake caused damage in Morelos and Puebla states and in Mexico State.
It struck while many people took part in an earthquake drill exactly 32 years after a quake killed thousands.
The country is prone to earthquakes and earlier this month an 8.1 magnitude tremor in the south left at least 90 dead.
The epicentre of the latest quake was next to Atencingo in Puebla state, about 120km (75 miles) from Mexico City, with a depth of 51km, the US Geological Survey said.
At least 54 people were killed in Morelos state alone, south of the capital, and 26 reported killed in Puebla state. Thirty are confirmed dead in Mexico City with another nine in Mexico State.
About two million people in the capital were without electricity and phone lines were down. Officials also warned residents not to smoke on the streets as gas mains could have been ruptured.
Mexico City Mayor Miguel Angel Mancera told TV network Televisa that rescue services were dealing with collapsed or badly damaged buildings at 44 locations.
The earthquake drill was being held in Mexico City on the 32nd anniversary of a quake that killed up to 10,000 people.
Earthquake alarms did sound, correspondents say, but some residents apparently thought they were part of the day of drills.
The prolonged tremor hit at 13:14 local time (18:14 GMT) and sent thousands of residents into the streets.
Jennifer Swaddle, a teacher at the British International School in Mexico City, told the BBC that part of her classroom collapsed after the earthquake hit.
"Something that started as a tremor quickly escalated into something where the classroom shook," she said.
"As we were leaving, the outside of my classroom wall fell, so there was a big pile of rubble. Luckily, fantastically, nobody was hurt, but it was incredibly frightening."
President Enrique Peña Nieto urged people to avoid the streets so emergency services could reach the most affected areas.
Panic on the streets
Mexico City is a city all too used to earthquakes. But this tremor, on the anniversary of another one that left thousands dead in 1985, was especially powerful.
It sent thousands of people into the streets, trembling, shaking, crying, and trying to reach their loved ones by phone.
As time passes it is becoming clear that there are going to be many victims. In the capital alone, about 30 buildings collapsed.
In one of the worst-affected areas I saw dozens of people desperately removing rubble because they believed someone was trapped
US President Donald Trump tweeted: "God bless the people of Mexico City. We are with you and will be there for you."
Canadian Prime Minister Justin Trudeau also tweeted his support following the "devastating news".