Russian media reported that 87 people were killed in the crash near Smolensk 06:56 GMT, and a regional governor was quoted as saying there were no survivors.
Polish officials said Mr Kaczynski was on board along with his wife Maria and several senior government figures.
Central bank governor Slawomir Skrzypek was also said to have been on board.
Ministry spokeswoman Irina Andrianova said it had been flying from Moscow to Smolensk, but had no details on the identities of those killed.
Smolensk regional governor Sergei Antufiev told Russian TV that no-one had survived.
"As it was preparing for landing, the Polish president's aircraft did not make it to the landing strip," he said.
According to preliminary reports, it got caught up in the tops of trees, fell to the ground and broke up into pieces.
Russian media carried claims that the plane's crew were at fault for the crash.
"The pilot was advised to land in Minsk, but decided to land in Smolensk," said Andrei Yevseyenkov, a Smolensk regional government spokesman.
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