The demonstrators, from protest group Kaputin, were demanding the release from prison of Kremlin critic Alexei Navalny and denounced the build-up of Russian troops near Ukraine's eastern border.
The protesters added a mock golden toilet brush to the effigy's hand and a roll of toilet paper in the other. Inscribed on the stand the words "naked killer".
Mock golden toilet brushes were also found hanging next to the entrance sign of the Russian embassy.
Toilet brushes became a symbol of pro-Navalny protests in February after the opposition leader published a video in which he and his allies alleged that an opulent palace belonged to the Russian leader.
The Kremlin has denied that Putin owned the palace, called the video an information attack on the president and suggested what it described as a "pseudo-investigation" was a scam designed to con gullible Russians into donating to Navalny's organisation.
Russia jailed Navalny for two-and-a-half years in February for parole violations he said were trumped up. He was arrested at the border as he returned to Russia from Germany where he had been recovering from a nerve agent poisoning.
State prosecutors in Moscow asked a court on Friday to label Navalny's anti-corruption group and regional headquarters "extremist" organisations, a move that would ban them and open up activists to long jail terms.
The move, if approved, would mark one of the most serious steps taken by authorities yet to target the network of groups set up by the staunch critic of Putin who is on hunger-strike as he serves his jail term.
The protesters also called on the Czech government to keep a pro-Western orientation and not order Russia's Sputnik V vaccine.