The Antonov An-26 had attempted to land during a training exercise when it caught fire just a mile from a military airport on Friday night.
The General Staff of the Armed Forces, Ruslan Khomchak, said that in addition to those killed, at least two people were seriously injured.
A total of 27 people were on the plane, according to the Ukrainian state emergency service.
Most of those on board were students from the Kharkiv Air Force University, which is run by the country’s defense ministry.
Deputy Interior Minister Anton Gerashchenko released a video showing the burning plane with smoke rising upwards.
Other photos showed rescuers inspecting the wreckage near Chuhuiv, about 400 km east of the Ukrainian capital, Kiev.
The cause of the crash is under investigation, but a pilot reported the failure of one of the two engines of the plane, according to Oleksiy Kucher, the governor of the Kharkiv region.
He told Interfax Ukraine that this would not have been a critical situation for an experienced pilot.
Some of the passengers managed to jump out of the plane while it was flying at low altitude, he added, which was confirmed by a witness on the Ukraine 24 news channel.
President Volodymyr Zelenskiy will visit the scene on Saturday.