The apparent drone attack caused Moscow’s airports to briefly suspend flights.
Russian officials said air defence forces had shot down two of the three drones over the wider Moscow region’s Mozhaisky and Khimki districts.
A third drone which was brought down lost control and crashed into a high-rise building under construction in the Moscow City business district, the ministry said. It said there had been no casualties.
Remote-controlled strikes in Russia have increased since a drone was destroyed over the Kremlin in May.
Russian state media reported that glass panes on three floors of the high-rise building had been damaged in the latest attack.
Ukraine has not responded to Russian accusations, including for two strikes near the Expo Centre in July.
It rarely takes responsibility for the attacks, but its officials see the drone strikes as a “fair” response to Putin’s unprovoked invasion of Ukraine in February last year.
The attacks have briefly disrupted flights and caused mostly minor damage to buildings.
Ukrainian president Volodymyr Zelensky has previously said of the strikes: “Gradually, the war is returning to the territory of Russia, and this is an inevitable, natural and fair process.”
The United States said it did not encourage or enable attacks inside Russia, a State Department spokesperson said after the latest incident.
However, the spokesperson added that it was up to Ukraine to decide how it chooses to defend itself from the Russian invasion, and that Russia could end the war any time by withdrawing from Ukraine.