Oleksiy Dmitrashkovsky said that the plane was shot down over the Luhansk region after launching an attack on rebels. The pilot ejected and was taken to a secure place, he said.
Further details about the incident or the condition of the pilot were not immediately available.
Fighting in Ukraine has escalated since the insurgency arose in April, with government troops steadily taking back rebel-held territory in the east.
The city of Luhansk is encircled by Ukrainian forces and is reportedly suffering from severe electrical outages and shortages of food and medicine. Donetsk, the largest rebel-held city, is also suffering through fighting including frequent shelling.
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Although the rebels have lost significant ground to Ukrainian forces in recent weeks, the downing of the fighter jet showed they retain substantial firepower.
In a video posted online this weekend, the leader of the self-proclaimed rebel government in the Donetsk region, Alexander Zakharchenko, was seen saying new military equipment was on its way from Russia. He said the shipment included tanks and some 1,200 fighters who have undergone training in Russia.
As fighting continued and the status of the Russian aid convoy remained uncertain, the foreign minister of Ukraine, Russia, Germany and France were expected to meet in Berlin today over the crisis.