According to a text accompanying a YouTube video, bassist Jared Hasselhoff performed the stunt during a concert in Kiev on July 30, one day before the Russian flag incident.
Kiev police said in a statement they had been informed about the incident on Monday and described Hasselhoff's actions as showing disrespect for the Ukrainian people.
The police said they had launched an investigation, classifying the way the flag had been used as "hooliganism" and an "outrage against state symbols".
A spokeswoman for Ukraine's Foreign Ministry described both flag stunts as "unacceptable".
"Such actions involving the desecration of state symbols cannot be justified by (their intended) shock value," she said.
Russia last week barred Bloodhound Gang, which is known for its sexually explicit songs and on-stage antics, from performing at a festival in the Krasnodar region by the Black Sea.
The band could also face criminal charges in Russia and a member of the upper house, the Federation Council, has called for the band's members not to be allowed to return to Russia.
Source: Yahoo News