The reported strikes temporarily disrupted flight operations at the major Vnukovo airport on Tuesday.
Zakharova described the alleged attacks as an "act of terrorism," blaming the Ukrainian government. Moscow Mayor Sergei Sobyanin said all detected drones had been eliminated.
"At this moment, the attacks have been repelled by air defense forces," Sobyanin said on his Telegram messaging channel.
Officials say several drones were intercepted near Moscow by air defenses. Another drone was reportedly shot down over the Kaluga region, some 190 kilometers (110 miles) from the capital.
Russia has reported numerous drone attacks on its cities during Russia's offensive in Ukraine, but the reports have increased in frequency in recent months. Kyiv, however, has repeatedly denied involvement in such strikes.
