Bridges were also destroyed and fires started, while some power and telecommunications links were cut, witnesses said.
Metro Television reported the roof of Padang airport had collapsed.
"Part of the roof of the arrival hall at the Padang airport collapsed but nobody was injured. The runway is okay. The airport has been closed but will reopen at 7am tomorrow," Hariyanto, an official of airport operating company Angkasa Pura II, said.
Rustam Pakaya, the head of the health ministry's disaster centre, said that a hospital was among the buildings that had been destroyed on Wednesday.
He said a field hospital was being prepared to assist the injured and medical teams were on their way from neighbouring provinces.
The 7.6-magnitude earthquake, which hit just off the coast of Western Sumatra province early in the morning, also triggered a landslide which cut off land access to the town.
Thousands of people are expected to spend the night in the open before a full assessment of the damage can be made in the morning.
Aburizal Bakrie, Indonesia's welfare minister, said authorities should prepare for the worst, adding damage could be on a par with an earthquake in Yogyakarta, central Java, in 2006 that killed 5,000 people and damaged or destroyed 150,000 homes.'Very strong'
"The earthquake was very strong," Kasmiati, who lives on the coast near to the epicentre, told The Associated Press news agency.
"People ran to high ground. Houses and buildings were badly damaged," she said. "I was outside, so I am safe, but my children at home were injured."
The Pacific Tsunami Warning Centre issued regional tsunami warning following the earthquake, but the warning was cancelled soon afterwards.
The Indonesian earthquake came just hours after a series of tsunamis caused death and devastation on the Pacific island nations of American Samoa and Western Samoa.
Padang, the capital of Indonesia's West Sumatra province, sits on one of the world's most active fault lines along the "Ring of Fire", where the Indo-Australia plate grinds against the Eurasia plate, creating regular tremors and sometimes earthquakes.
The low-lying city of about 900,000 people was badly hit by an 8.4 magnitude quake in September 2007, when dozens of people died and several large buildings collapsed.
"It is a city that has been under threat of a huge earthquake for quite a long time," Al Jazeera's Step Vaessen, reporting from Jakarta, said.
"Padang was sort of next on the list and experts have been warning of a major earthquake in that area for quite a long time. We travelled there a few years ago and saw that they did not seem prepared for any sort of major disaster."
In 2004, a 9.15 magnitude earthquake, with its epicentre roughly 600km northwest of Padang, caused a tsunami that killed 232,000 people in Indonesia's Aceh province, Thailand, Sri Lanka, India, and other countries across the Indian Ocean.