The building was located in Chasiv Yar, near the city of Kramatorsk in the Donetsk region.
The Ukrainian government has said it planned to raise a "million-strong army" equipped with North Atlantic Treaty Organisation (NATO) weapons to retake the south of the country from Russian troops occupying the region.
However, the comments by Ukraine’s defence minister, Oleksii Reznikov, are being seen as more of a rallying cry than a concrete plan for a counter-offensive.
Russia is making progress in taking territory in the eastern Donbas region, as there was an attack on a block of flats on Sunday that killed at least 22 people while more residents are still missing.
The building was located in Chasiv Yar, near the city of Kramatorsk in the Donetsk region.
The remarks of a counter-attack may be more of a rallying cry than a set plan, as there would not be any operational surprise in this attack now that it has been announced.
Ukraine may be announcing this counter attack to force Russia to commit troops to the southern areas of the country away from other areas currently being attacked.
Reznikov also said that retaking the country's southern Black Sea coast was vital to the country's economy.
In his interview with The Times newspaper, the minister said weapons deliveries needed to be sped up.
He praised the UK for being "key" in the transition from providing Ukraine with Soviet-era weapons to the more effective NATO-standard air defence systems and ammunition.
"We need more, quickly, to save the lives of our soldiers. Each day we're waiting for howitzers, we can lose a hundred soldiers," he said.
The defence minister added, "We have approximately 700,000 in the armed forces and when you add the national guard, police, border guard, we are around a million-strong."
However, analysts have cautioned against taking the figure of one million at face value.
"It's not a million-strong force that will be conducting a counter-attack," Dr Jack Watling, senior research fellow at the Royal United Services Institute, told the BBC.
"Normally you would want operational surprise when you launch a counter-attack, so announcing it publicly is partly about forcing the Russians to have to commit resources more widely to guard against this threat."