Panicked workers fled from office buildings and clouds of dust rose up from the crumbling facades of damaged buildings after the 7.1 magnitude quake struck.
The tremors came hours after preparation drills were held on the anniversary of a devastating 1985 earthquake that killed more than 5,000 people in the city.
At least 30 people died in the capital, while there were reports of others trapped in collapsed and burning buildings.
TV footage showed rescuers frantically trying to dig into rubble with pickaxes.
Buildings fell at 44 places in the city, according to Mayor Miguel Angel Mancera.
Speaking minutes after the earthquake struck, resident Georgina Sanchez sobbed: "I'm so worried. I can't stop crying. It's the same nightmare as in 1985."The US Geological Survey said the quake was centred near Raboso in Puebla state, 76 miles (123km) southeast of Mexico City.
A civil protection official in Puebla said two people had been killed after a school collapsed, while Mexico state's governor confirmed eight deaths, including a quarry worker killed by a rockslide and another victim hit by a falling lamppost.
Officials asked people not to smoke in the streets of Mexico City - which has a population of 20 million - warning of possible ruptured gas pipes.
TV footage showed rescuers frantically trying to dig into rubble with pickaxes.
Buildings fell at 44 places in the city, according to Mayor Miguel Angel Mancera.
Speaking minutes after the earthquake struck, resident Georgina Sanchez sobbed: "I'm so worried. I can't stop crying. It's the same nightmare as in 1985."The US Geological Survey said the quake was centred near Raboso in Puebla state, 76 miles (123km) southeast of Mexico City.
A civil protection official in Puebla said two people had been killed after a school collapsed, while Mexico state's governor confirmed eight deaths, including a quarry worker killed by a rockslide and another victim hit by a falling lamppost.
Officials asked people not to smoke in the streets of Mexico City - which has a population of 20 million - warning of possible ruptured gas pipes.
Mexico City International Airport suspended operations, while electricity and phone lines were down in parts of the capital.
"We got out really fast, leaving everything as it was and just left," said Rosaura Suarez, as she stood with a crowd on the street.
Alfredo Aguilar, 43, said the quake was "really strong - buildings started to move".
He added that he saw a woman fainting as "people started to run."
"We got out really fast, leaving everything as it was and just left," said Rosaura Suarez, as she stood with a crowd on the street.
Alfredo Aguilar, 43, said the quake was "really strong - buildings started to move".
He added that he saw a woman fainting as "people started to run."