At least two people were injured and buildings were damaged in a raid by up to eight unmanned bombers.
Russia described the onslaught as a "terrorist attack".
Ukraine denied responsibility but the blitz came days after its chief intelligence officer warned of retaliation for airborne strikes on Kyiv.
One woman was killed and several other people injured when Russia bombed the Ukrainian capital in the early hours of yesterday.
Downing Street denied British-supplied weapons were used in the Moscow raid.
Natia Seskuria, an expert in Russian security at London's Royal United Services Institute, said the incident could undermine Vladimir Putin's domestic support.
Audacious
She told the BBC: "It raises a lot of insecurities despite the propaganda which we know has been working 24/7 to justify the Russian war effort.
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