The terrifying ordeal occurred when the plane flew through a pocket of "clean air" turbulence - so-called because there is no cloud warning of its presence - shortly before landing in Bangkok after midnight, the airline said.
Denis Antonyuk, an official at Russia's embassy in Bangkok, said 24 Russian nationals and three Thais were injured.
"Fifteen Russians and two Thais are still in hospital," he told AFP, adding the rest had been discharged.
Passenger phone footage broadcast by Rossiya 24 state television channel showed a scene of chaos inside the cabin, with injured passengers on the floor, smears of blood on luggage racks and oxygen masks hanging down.
"We were hurled up into the roof of the plane, it was practically impossible to hold on," a passenger who gave her first name Yevgenia, told Rossiya 24 by phone.
"It felt like the shaking wouldn't stop, that we would just crash," she added.
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.
"All the injured were taken to a local hospital with injuries of varying degrees of severity - mainly fractures and contusions. Some need an operation," the Russian embassy in Bangkok said in a statement.
Officials 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 ruble weakened but they have since bounced back.
Last year just over one million Russians visited the country, most flocking to the southern beach resorts.
Early May is an especially popular time of the year for Russians to head abroad with two public holidays in the first two weeks of the month.