No injuries were life-threatening, but several passengers suffered broken bones and three needed surgery, Russian officials said.
A passenger described being "hurled" up to the ceiling, trying to cling on amid shaking which "wouldn't stop".
The turbulence occurred in clear skies, which meant the crew were not able to warn passengers, the airline said.
"The reasons behind the injures were that some of the passengers had not had their seatbelts fastened," Aeroflot said in a statement.
