Bek Air Flight Z2100 was en route from Almaty to Nur-Sultan when it lost altitude and crashed into a concrete building at 7.22 a.m.
"Fourteen people died at the scene. One person died in the hospital," TASS News Agency quoted Tleukhan Abildaev, Head of Kazakhstan's Public Healthcare Department, as saying.
Medical assistance has been provided to 60 people who survived the crash, according to the Almaty International Airport administration.
Rescuers have taken 24 people to hospitals following the crash, the press service of Kazakhstan's Interior Ministry reported.
"According to preliminary data, 24 people were injured and taken to the hospitals. The identity of seven of those killed in the accident has been established," the press service said.
The airport was working as usual and there were no changes in the flight schedule because of the crash, it said.
There was nobody inside the building that the plane collided with, TASS News Agency reported citing Deputy Director of the Almaty Department for Emergency Situations Yerlan Alibekov as saying.
"The plane's fuselage collided with a residential house under construction. Fortunately, there was nobody inside the building," Alibekov said, adding that the rescue operation was aksi completed.
The Bek Air fleet consists of Fokker 100 planes.
Until the reasons of the crash were established, use of other aircraft of this type has been temporarily suspended.
A governmental commission has been set up to investigate the reasons of the crash.
Meanwhile, Kazakhstan's President Qasym-Jomart Toqayev expressed "deep condolences" to the victims' relatives, the BBC reported.
He also said that "all those responsible will be severely punished in accordance with the law".
Bek Air was founded in 1999, targeting VIP flight operations, according to the company's website. Nowadays, it describes itself as Kazakhstan's first low-cost airline.
( With inputs from IANS )