Satellite photos showed the aftermath of the attack, Ukraine's main military intelligence service said.
If confirmed, it would mark Ukraine's first known successful strike on a twin-engine Su-57 stealth jet, lauded as Russia's most advanced fighter plane.
In one photo, black soot marks and small craters can be seen dotting a concrete strip around the parked aircraft.
According to the Main Intelligence Directorate of Ukraine's Ministry of Defence, the strike took place on Saturday at the Akhtubinsk base in southern Russia, 589km from the front line.
The Ukrainian agency said the plane, which is capable of carrying stealth missiles across hundreds of kilometres, was among "a countable few" of its type in Russia's arsenal.
According to reports by Russian agencies, the air force obtained "more than 10" new Su-57s last year and has placed an order for a total of 76 to be delivered by 2028.
A spokesman for Ukraine's military intelligence, Andriy Yusov, hours later said on Ukrainian TV that the attack may have damaged two Su-57 jets parked at the base and also wounded Russian personnel.
He did not immediately give any evidence to support the claim.
ВОГОНЬ ЗАПЕКЛИХ НЕ ПЕЧЕ!— Генеральний штаб ЗСУ (@GeneralStaffUA) 44 окрема артилерійська бригада імені гетьмана Данила Апостола pic.twitter.com/Tm8peRl4DcJune 8, 2024
Ilya Yevlash, a spokesman for Ukraine's air force, told Ukrainian media in April that Russia was trying to keep its Su-57 fleet "at a safe distance" from Ukrainian firepower.
The strike comes after the United States and Germany recently authorised Ukraine to hit some targets on Russian soil with the long-range weapons they are supplying to the country's forces.
Ukraine has already used US weapons to strike inside Russia under newly approved guidance from President Joe Biden that allows US arms to be used for the limited purpose of defending Kharkiv, Ukraine's second-largest city.
But the airstrip's distance from Ukraine, as well as unofficial comments from Russia, point to the likely use of Ukrainian-made drones.
Since Russia's full-scale invasion more than two years ago, Ukraine has ramped up domestic drone production and used the munitions to strike deep inside Russia.
Russia's Su-57 fleet has been largely absent from the skies over Ukraine, and has instead been used to fire long-range missiles across the border.
The United Kingdom Ministry of Defence said in an intelligence briefing last year that Russia is likely trying to avoid "reputational damage, reduced export prospects, and the compromise of sensitive technology" that would come from losing any Su-57 jets in enemy territory.
Elsewhere, Ukrainian forces kept up drone attacks on Russia's southern border regions, according to local Russian officials.
Three drones hit Belgorod province late on Saturday, damaging a power line and blowing out windows but causing no casualties, Governor Vyacheslav Gladkov said.
Another five drones and a Ukrainian-made missile were brought down over the region on Sunday, the Russian Defence Ministry said.
Across Ukraine's front-line provinces, Russian shelling killed at least three civilians and wounded at least nine others on Saturday and overnight, according to reports by regional officials.
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