Alexei Gorinov, 60, was arrested in April after he was filmed criticising the invasion in a city council meeting.
Under the post-invasion law, anyone who spreads "fake news" about the military faces up to 15 years in jail.
Russians are banned from using the word war to describe the invasion.
President Vladimir Putin has instead coined the phrase "special military operation", although he spoke of the "war in the Donbas" in remarks to parliamentary leaders on Thursday.
Human rights activist Pavel Chikov said Gorinov's sentence was the first jail term under the new law. Until now judges have only handed down a fine or a suspended sentence.
Judge Olesya Mendeleyeva ruled he had carried out his crime "based on political hatred" and had misled Russians, prompting them to "feel anxiety and fear" about the military campaign.
Appearing in court in northern Moscow, Gorinov held up a piece of paper with words he had written in pen: "Do you still need this war?" A security official held up his hands to try to obscure the message.
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