Andrei Lysenko also said Ukrainian troops had been fired upon by missiles from a village just inside Russia.
Officials in Kiev have recently accused Russia's armed forces of being directly implicated in attacks on Ukrainian troops battling an insurgency near the border.
Lysenko said in a televised briefing that the pilot of the Sukhoi-25 jet that was hit on Wednesday evening was forced to bail out after his jet was shot down. He provided no further details.
Moscow denies Western charges that is supporting the separatists in Ukraine or sowing unrest in its neighbour.
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On Monday, Ukraine said one of its military transport planes carrying eight people was shot down by a missile fired from Russian territory.
Security Service chief Valentyn Nalyvaichenko said he had "unconditional evidence" that Russia was involved in downing the craft.
Rebels claimed to have shot that plane down.
Russia's benchmark MICEX was down 2.6 per cent in early afternoon trading Thursday upon news of the sanctions while Russia's biggest oil company, Rosneft, was nearly 5 per cent down.
The US sanctions target two major Russian energy firms including Rosneft, a pair of powerful financial institutions, eight weapons firms and four individuals.
The US penalties, however, stopped short of the most stringent actions the West has threatened, which would fully cut off key sectors of Russia's oil-dependent economy.