The monument, erected a day before Russia's Cosmonautics Day celebrated on April 12, is a two-meter (6.5 feet) high space rocket with Laika proudly standing on top.
The three-year-old mongrel, originally named Kudryavka or 'little curly-haired one,' was selected from an animal shelter to become the first living passenger to fly on the Soviet spacecraft Sputnik 2.
Laika was launched into space on November 3, 1957 and died a few hours later from overheating. Officials said she died due to a lack of oxygen, but the true cause of death was only made public in October 2002.
The experiment, which marked its 50th anniversary last year, paved the way for human spaceflight and provided scientists with information on how living organisms become accustomed to space environments.
At the unveiling ceremony the head of the Institute of military medicine, Igor Ushakov, said: "I'm looking at the monument and indeed recognize Laika. She is glancing at the house where the pre-flight preparations and training took place."
Three years after Laika's death her successors, Belka and Strelka, went into space aboard Sputnik 5 safely returning to Earth.
Russia celebrates Cosmonautics Day on April 12 in honor of the historic first manned space flight made by Soviet cosmonaut Yuri Gagarin in 1961.