The cause of the crash is being investigated.
The plane came down about 2km (1.2 miles) from a military airport in the town of Chuhuiv, the emergency ministry officials say.
There is no suggestion that the crash is linked to the conflict in eastern Ukraine. Chuhuiv is about 100km (60 miles) from the front line where government forces are fighting pro-Russian separatists.
Fire broke out at the site and was later extinguished.
"It's a shock," Deputy Interior Minister Anton Gerashchenko told AFP news agency. "At the moment it's impossible to establish the cause."
An investigation is under way. President Volodymyr Zelensky is due to travel to the region on Saturday.
Kharkiv regional governor Oleksiy Kucher said preliminary information suggested that one of the pilots had reported failure in one engine before the crash, but that this should not have been a critical situation, according to the Interfax-Ukraine news agency.
An eyewitness told Reuters news agency he had seen a man in flames running from the wreckage.
"Another car stopped behind us. We took a fire extinguisher and ran with another driver to help him," he said.
BBC