According to the Chancery of the Lithuanian Orthodox Archdiocese, the stickers were found posted on the Cathedral of the Assumption of Our Lady in Vilnius and on nearby pillars.
Parishioners found the stickers when they came to the church for the morning prayer service, it said.
Loreta Kairiene, the spokeswoman for the Vilnius District Police, told BNS that the incident in Maironio Street, in the capital's Old Town, was reported to the police at 8:00 a.m.
"The deacon reported to the police that the stickers read in Cyrillic, 'Patriarch Kirill is a liar and a sinner', and depicted Putin and Kirill splashed with blood," she said.
Officers went to the scene and spoke to the deacon. He submitted a statement.
The capital's police are investigating the incident and consider initiating administrative proceedings, according to the spokeswoman.
In a similar incident, a sheet of paper with Russian swear words written on it was found on the wall of an Orthodox church in Lithuania's second-biggest city of Kaunas earlier this month.
"Such terror and intimidation against our parishioners are totally unacceptable, and we call on the authorities to take decisive measures to ensure their protection," Metropolitan Innokentiy, the head of the Lithuanian Orthodox Church, said in a statement on Thursday.
"The escalation of the atmosphere of ill will and hostility around our Church is not in the interests of Lithuanian society. We are ready for dialogue with the government, for which we pray daily in all the churches of the Lithuanian Orthodox Church," he added.
Innokentiy last week suspended five Orthodox priests from their duties and referred the case of Gintaras Sungaila, one of them, to the Moscow Patriarchate to decide whether to strip the priest of his rank.
The priests have criticized the Russian Orthodox Church and Patriarch Kirill of Moscow for their support of Russia's war in Ukraine.
The Lithuanian Orthodox Church denies that the priests were suspended because of their position on the war and says it condemns Russia's actions in Ukraine.
The Lithuanian Orthodox Church, one of Lithuania's nine traditional religious communities, is a metropolitanate within the Patriarchate of Moscow and All Russia.
Some Lithuanian Orthodox priests have asked the patriarch of Constantinople to allow them to switch jurisdictions.