A Moscow court handed down the ruling after Kremlin-connected billionaire Alisher Usmanov challenged accusations he gave a bribe to a foundation linked to Medvedev.
A Moscow court handed down the ruling after Kremlin-connected billionaire Alisher Usmanov challenged accusations he had given a mansion as a bribe to a foundation linked to Medvedev.
Anti-corruption campaigner Navalny, who intends to run against President Vladimir Putin in next year's election, said he was unsurprised at the ruling and he would appeal.
The video accusing Medvedev of amassing a shadowy property empire -- viewed 21 million times on YouTube -- prompted the biggest protests in years against the Kremlin in March. Navalny has called for a new round of demonstrations on June 12.
However Judge Marina Vasina said it gave incorrect information and discredited Usmanov's "honour, dignity and business reputation," RIA Novosti news agency reported.
She ordered Navalny to publish a retraction and remove the video.
"We didn't doubt there would be such a decision," Navalny told journalists outside the court, insisting he would not take the video down.
"The investigation is based on facts," he added.
Usmanov has accumulated a fortune of $15.2-billion from metallurgy and interests in social media, according to Forbes magazine's rich list, and owns 30 percent of London football club Arsenal.
His lawyer Genrikh Padva said after the decision that he was "very glad we managed to defend someone's good name," news agency RIA Novosti reported.
The Russian interior ministry said that it had looked into the claims made by Navalny and found no crime.
Navalny, a lawyer, came to fame at the head of anti-Putin rallies in the winter of 2011 and 2012. His team works on exposing the lavish lifestyles of the Kremlin elite.
But his participation in next year's election -- which Putin is widely expected to compete in and win -- is in doubt because of a suspended sentence for a criminal conviction he says was politically motivated.
Navalny had asked Medvedev to give evidence at the two-day trial, a request the judge threw out.