In addition to Moscow, the governors of other Russian cities, including Penza and Voronezh, also said drone strikes targeted their areas on Tuesday night.
Unconfirmed reports from Russian military bloggers suggest that the windows of an apartment south of Moscow were shattered by a drone strike.
For the second night in a row, Russia reported drone strikes by Ukraine. Earlier on Monday, the Russian Defense Ministry said it had destroyed 26 Ukrainian drones overnight.
Ukraine has not yet commented on the matter, but the mayor of Kharkiv has claimed that Russia also carried out drone attacks on his city and the surrounding area of Kiev at night.
Kiev has carried out several drone strikes on Moscow since Russia's full-scale invasion of Ukraine more than three years ago, with its biggest drone strike in March killing three people.
The drone attack in Moscow came to light on Monday after reports emerged that Ukrainian troops were attempting to advance into Russia's Kursk region.
Kiev, citing Ukrainian military officials, said it hit a drone command unit near the village of Teotkino in Russia's Kursk region on Sunday.
Last April, Moscow said it had regained control of the entire region nine months after Ukrainian forces launched a surprise offensive. But Kiev insists its troops are still operating across the border.
Russian officials also said that an electrical substation in the city of Rylsk in the Kursk region was knocked out of power by the Ukrainian attack on Monday.
According to Alexander Khinshtein, the acting governor of the Kursk region, in a post on the Telegram messaging app, two transformers at the Rylsk substation were damaged and two teenagers were injured in the explosion.
Several Russian military bloggers also reported that Ukrainian forces had attempted to enter the village. They posted images of vehicles breaking through tank traps on the border - which the BBC has not yet been able to verify.
According to bloggers, Ukrainian forces fired missiles across the border on Monday and crossed minefields in special vehicles.
"The enemy blew up the bridge with rockets at night and launched an attack with armored groups in the morning," Reuters news agency reported, citing blogger Arvivoenkar.
"Mine clearing vehicles have begun entering the minefields, followed by armored vehicles with soldiers. Intense fighting is ongoing on the border."
"Nine months after the start of the Kursk operation, the Ukrainian Defense Forces maintain a military presence on the territory of the Kursk region of Russia," Ukraine said in a statement on Monday.
There has been no official response from Moscow, but some military bloggers have also published maps showing opposition forces attempting to cross the border in two places towards Teotkino - where the drone command unit was hit.
Meanwhile, local authorities in the Sumy region, about 12 kilometers from Teotkino in northeastern Ukraine, have urged people to evacuate two settlements, Reuters reported.
Ukraine originally made a surprise incursion into Kursk in August 2024. At the time, it claimed to have carried out the incursion in the hope of creating a buffer zone, securing Sumy and surrounding areas, and using it as a bargaining chip in future negotiations.
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