Swastikas were painted on the Remember Memorial to genocide victims - civilians killed in the Nazi occupation of 1941-1943 - in Novomoskovsk, Ukraine's Dnipropetrovsk region, the regional police department told Interfax.
It said a hooliganism case had been opened.
This crime has an anti-Semitic flavor, monument initiator, Dnipropetrovsk Council deputy Serhiy Reznyk told Interfax-Ukraine.
"Those who committed this act of hooliganism are morally defective," he said.
The memorial was unveiled on May 22 by the initiative of the city Jewish community. It carries the names of people executed by the Nazi, including Jews. Some of the inscriptions are in Yiddish.
KyivPost