The assembly in Lvov passed a decision on Thursday to remove the statue from a square in Stryi and place it in a museum of Soviet totalitarianism, saying the statue had no historical or cultural value.
Lyubov Sliska, deputy speaker of Russia's lower house of parliament, said such decisions could only be made by a "criminal regime."
"They have long turned a blind eye to Nazi marches, portraying those who massacred people as heroes," Sliska said, adding the decision revealed lawmakers' disrespect for the soldiers who liberated Ukraine.
Lawmakers in the fiercely nationalistic Lvov region argued on Thursday that such statues - the monument depicts a soldier holding a sword in one hand and a child in the other - are scattered across Ukraine.
Local communists said on Friday they would protest against the decision, which they said ran counter to a law making authorities responsible for the preservation of World War II monuments.
Western Ukraine was the stronghold of the Ukrainian Insurgent Army, a nationalist group initially set up to protect ethnic Ukrainians from Poles, engaged in guerrilla fighting with Soviet troops, collaborating with Nazi Germans during the war.
President Viktor Yushchenko has sought recognition for the group, and a statue to one of its founders, Stepan Bandera, was unveiled in Lvov in 2007.
The relocation of the Bronze Soldier, a Soviet-era monument to the Red Army, in Estonia in 2007 sparked violent protests from ethnic Russians. One person was killed and several dozen injured in clashes with police. Moscow issued strong protests with some lawmakers calling for cutting diplomatic ties with Tallinn.
