The meteorite, which weighed about 10 tons, broke through the atmosphere around 9:20 a.m., traveling at a speed of 33,000 mph, ITAR-Tass reported.
At least 750 of the injured were in the city of Chelyabinsk, Der Spiegel reported.
Reports indicated most of the injuries were caused by broken glass and flying objects.
A state of emergency was declared.
A spokeswoman for the Russian Ministry of Emergency Situations told The New York Times the meteorite broke apart and fell in several places.
"I saw a flash in the window, turned toward it and saw a burning cloud, which was surrounded by smoke and was going downward," said Maria Polyakova, 25, of the Park-City Hotel in Chelyabinsk, 90 miles east of Moscow.
Gas supplies were cut off to hundreds of homes as a safety precaution and about 20,000 emergency response workers were called out, RIA Novosti reported.
Russia's national space agency, Roscosmos, confirmed that the strike involved one large object and not several smaller ones.
A search team found an impact crater on the outskirts of a city about 50 miles west of Chelyabinsk, indicating the meteor did not explode in the atmosphere, the governor of Chelyabinsk said.
One government expert told a Moscow radio station he believed it may have been a bolide, a type of meteor that explodes in the atmosphere because of its composition or angle of entry.
About 10,000 police officers were dispatched to search for and retrieve pieces of the object.
"Current information, which is not yet complete nor confirmed, points to a small asteroid," said Detlef Koschny, Head of Near-Earth Object activity at the European Space Situational Awareness office.
"There is no way it could have been predicted with the technical means available today. What can be said with near certainty is that this object has no connection with asteroid 2012 DA14."
2012 DA14 is a small asteroid that was expected to make a close fly-by late Friday with no chance of striking Earth, NASA's website said