The aircraft encountered a severe pocket of "clean air" turbulence -- so-called because there is no cloud warning -- before landing just after midnight, the Russian national carrier said in a statement.
Denis Antonyuk, an official at Russia's embassy in Bangkok said 24 Russian nationals and three Thais were injured.
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"Fifteen Russians and two Thais are still in hospital," he told AFP, adding the rest had been discharged.
The head of the Russian embassy's consular department Vladimir Sosnov told RIA Novosti news agency that some of the injured were undergoing operations but he could not give exact numbers.
He added that none of the injuries were life-threatening.
Russia state television Channel 1 said some passengers suffered multiple injuries.
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Thai police at Bangkok's Suvarnabhumi airport did not respond to requests for comment.
Thailand has become a very popular destination for sun-seeking Russian tourists with dozens of flights a day from across the country.
Numbers dropped off a few years back when the rouble weakened but they have since bounced back.
Last year just over one million Russians visited the country, most flocking to the southern beach resorts.
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