"The incident occurred on the territory of a military unit in the Kharkov region," the source said, adding that the explosions were still continuing.
The Ukrainian Defense Ministry said in a statement that all personnel had been evacuated and no casualties had been reported.
"As of 7:00 p.m. Moscow time [15:00 GMT] all depot personnel have been evacuated to a safe distance," the statement said.
The ministry also said that the fire at the depot, which stored some 95,000 metric tons of ammunition, was caused by forest fires in the Kharkov Region.
A fire last month at another Soviet-era depot, in the central Uzbek town of Kagan, resulted in a series of explosions, which killed three and wounded 21.