The plane caught fire while attempting to land in a remote Russian region north of the Arctic Circle. Twenty-four people survived, the ministry said.
The An-24 two-engine turboprop aircraft crashed on final approach to an airport near the oil port of Varandei in the Nenets autonomous region on Russia's Pechora Sea coast, some 1800 km northeast of Moscow, on Wednesday.
There were 46 passengers and seven crew members on board, Emergency Situations Ministry spokesman Sergei Vlasov said. Ten of the survivors were hospitalised in critical condition, he said.
Another ministry spokesman, Viktor Beltsov, said 19 of the survivors, including those gravely injured, were evacuated by helicopter to the regional capital, Naryan-Mar, and that five who were virtually unhurt were taken to Varandei.
The passengers were employees and contract workers for affiliates of Russia's largest oil company, Lukoil, who were on their way to begin work stints.
The airliner, which belonged to the small Russian private carrier Regional Airlines, was approaching Varandei airport in fine weather when it banked and slammed into the ground after the tail section began to fall apart, officials said.
The plane, which had taken off from the city of Ufa in the southern Ural Mountains region, made stopovers in the cities of Perm and Usinsk on its way north to Varandei.
The An-24 is a Soviet-era turboprop airliner for short and medium routes which was built in the 1960s.