The crash added to a string of transport disasters in Russia, including the sinking of a riverboat on Sunday in which as many as 128 were killed.
The Antonov-24 (AN-24), a Soviet-designed aircraft, was forced to land on the River Ob in Russia's Tomsk region after its left engine caught fire in mid-flight.
A spokesman for Russia's Federal Investigative Committee was quoted by state-run RIA news agency as saying that the plane had lost its tail upon impact with the water.
The aircraft was travelling from the regional capital of Tomsk to Surgut, also in Siberia, when the crew sent distress signals.
"There were 37 people on board, among them one baby," said Emergencies Minister Sergei Shoigu. "Casualties totalled 35, five of whom died. Thirty have been hospitalised."
President Dmitry Medvedev suggested at a meeting with officials, including the transportation and emergencies ministers, that the accident showed that the AN-24 model should be taken out of service.
"I have been recently talking about the state of our air fleet. All that I have said regarding Tupolev-134 is applicable to AN-24 planes," said Medvedev, referring to another Soviet-era aircraft that is due to be permanently grounded.
Last month 45 people died in a plane crash in northwest Russia, making it the worst air disaster in over a year.
That accident followed the crash of Polish President Lech Kaczynski's official plane near the western city of Smolensk in a thick fog in April 2010, killing him and all 95 others on board.
