Ukraine has already been using Atacms in Russian-occupied areas of its own territory for more than a year.
The missiles can hit targets at a range of up to 300km (186 miles) and are difficult to intercept.
Kyiv is now able to strike deeper into Russia using the missiles, including around the Kursk region, where Ukrainian forces hold over 1,000 sq km of territory. Ukrainian and US officials reportedly expect a counter-offensive in the region.
In a statement, Russia’s defence ministry said the strike was launched at 03:25 (00:25 GMT).
A fire caused by fallen debris from one of the missiles was quickly extinguished and there were no casualties, it said.
Ukraine’s military earlier confirmed that it had struck an ammunition warehouse in the Russian region of Bryansk, but it did not specify whether Atacms were used.
It said the attack, on a depot around 100km from the border near the town of Karachev, caused 12 secondary explosions.
Meanwhile, earlier on Tuesday, Putin approved changes to Russia’s nuclear doctrine, setting out new conditions under which the country would consider using its arsenal.
It now says an attack from a non-nuclear state, if backed by a nuclear power, will be treated as a joint assault on Russia.
