The aircraft are known to carry the hypersonic Khinzhal missiles that are used in long-range attacks on Ukrainian cities.
Atesh, a group of pro-Kyiv partisans in the area, said the main missile and artillery depots at the airbase were damaged.
The long-range barrages came as Ukrainian forces struggle to contain a new Russian offensive in the north-eastern Kharkiv region.
Volodmyr Zelensky, the Ukrainian president, said his forces had “stabilised” the new front lines as of Friday, a week after he first confirmed the Russian cross-border offensive.
He told journalists that Russian forces had advanced six miles into the region since launching the attack.
But Gen Oleksandr Syrsky, the Ukrainian commander-in-chief, warned: “We understand that there will be tough battles ahead and the enemy is preparing for it.”
He also said the fighting could soon stretch to the northern Sumy region, which borders Belarus, as Moscow seeks to stretch Ukraine’s reserves.
In a boost for Kyiv’s battle-stricken forces, Mr Zelensky said on Friday that his men had enough artillery shells for the first time in the war.
The supplies are likely a result of American aid arriving in the country after Washington signed off on a $60 billion aid package last month.