(BBC) - Most of those hurt, in the Chelyabinsk region where the meteor fell, suffered cuts and bruises but at least 46 remain in hospital.
A fireball streaked through the clear morning sky, followed by loud bangs.
President Vladimir Putin said he thanked God no big fragments had fallen in populated areas.
A large meteor fragment landed in a lake near Chebarkul, a town in Chelyabinsk region.
The meteor's dramatic passing was witnessed in Yekaterinburg, 200km (125 miles) to the north, and in Kazakhstan, to the south.
"It was quite extraordinary," Chelyabinsk resident Polina Zolotarevskaya told BBC News. "We saw a very bright light and then there was a kind of a track, white and yellow in the sky."
"The explosion was so strong that some windows in our building and in the buildings that are across the road and in the city in general, the windows broke."
Officials say a large meteor partially burned up in the lower atmosphere, resulting in fragments falling earthwards.
Thousands of rescue workers have been dispatched to the area to provide help to the injured, the emergencies ministry said.
The Chelyabinsk region, about 1,500km (930 miles) east of Moscow, is home to many factories, a nuclear power plant and the Mayak atomic waste storage and treatment centre.
Chelyabinsk's health department said 985 people had sought medical treatment, including 204 children, Russia's Interfax news agency reports. Two people in the town of Kopeysk were in a serious condition, it added.
The governor of Chelyabinsk region, Mikhail Yurevich, was quoted elsewhere as saying 950 people had been hurt, two seriously.
Mr Putin promised "immediate" aid for people affected, saying kindergartens and schools had been damaged, and work disrupted at industrial enterprises.
Many children were at lessons when the meteor fell at around 09:20 (03:20 GMT).
Video posted online showed frightened, screaming youngsters at one Chelyabinsk school, where corridors were littered with broken glass.
Chelyabinsk resident Sergei Serskov told BBC News the city had felt like a "war zone" for 20 to 30 minutes.
"I was in the office when suddenly I saw a really bright flash in the window in front of me," he said.
"Then I smelt fumes. I looked out the window and saw a huge line of smoke, like you get from a plane but many times bigger."
"A few minutes later the window suddenly came open and there was a huge explosion, followed by lots of little explosions."
In Yekaterinburg, 36-year-old resident Viktor Prokofiev was driving to work when he witnessed the event.
"It was quite dark, but it suddenly became as bright as if it was day," he was quoted by Reuters as saying.
"I felt like I was blinded by headlights."
Debris also reportedly fell on the west Siberian region of Tyumen.
Governor Yurevich reported that the meteor had landed in a lake 1km outside Chebarkul, which has a population of 46,000.
A Russian army spokesman said a crater 6m (20ft) wide had been found on the shore of the lake.