Rafal Leskiewicz, the institute's spokesman, said that in March, when a decision was announced to remove them, there were still 60 standing. The monument in Brzeg marks the 24th to be demolished.
He said it was important to remove such memorials because of Russia's war in Ukraine, but also because a Polish law in 2015 calls for them to be removed.
"It is impossible to keep such monuments in the public sphere," Leskiewicz told The Associated Press.
The work to dismantle the Brzeg monument is expected to last several days, he said.
Poland, which lies on Ukraine's western border, has been a key ally to Kyiv, sending military and humanitarian aid into the war-torn country. It has also become a place of exile for more Ukrainian refugees than any other single country.
The development in Poland comes after Estonia's government last week started removing a Soviet World War II monument from near a city on the Russian border as part of a wider effort, prompted by Russia's invasion of Ukraine, to dismantle remaining Soviet-era symbols.