They say the Bek Air aircraft went down shortly after taking off at Almaty airport on Friday morning local time.
Emergency service personnel have rushed to the scene and seven deaths have been confirmed. Survivors are being evacuated, the airport said.
The plane was en route from Almaty, Kazakhstan’s largest city, to the country’s capital of Nursultan.
Almaty’s airport said there were 95 passengers and five crew on board.
It said the plane lost height at 07:22 local time (01:22 GMT), before striking a concrete barrier and crashing into a two-storey building.
There was no fire upon impact.
Footage has emerged of rescuers working at the scene. In it, a woman can be heard calling for an ambulance.
A special commission will be set up to determine the cause of the crash.