The drone attack, which follows previous similar raids on the Russian capital, was the first known assault on the city since an abortive mutiny launched 11 days ago by mercenary chief Yevgeny Prigozhin.
His Wagner troops marched on Moscow in the biggest - although short-lived - challenge to Russian President Vladimir Putin in more than two decades of his rule.
Authorities in Ukraine, which generally avoids commenting on attacks on Russian soil, did not say whether it launched the drone raid.
The Russian Defence Ministry said that four of the five drones were downed by air defences on the outskirts of Moscow and the fifth was jammed by electronic warfare means and forced down.
There were no casualties or damage, Moscow mayor Sergei Sobyanin said.
The drone attack prompted authorities to temporarily restrict flights at Moscow's Vnukovo airport and divert flights to two other Moscow main airports.Â
Vnukovo is about 15km southwest of Moscow.
The raid came as Ukrainian forces have continued probing Russian defences in the south and the east of their country in the initial stages of a counteroffensive.
Oleksiy Danilov, the secretary of Ukraine's Security and Defence Council, said that the military was currently focusing on destroying Russian equipment and personnel, and that the past few days of fighting have been particularly "fruitful".
He provided no evidence and it was not possible to independently verify it.
The Ukrainian forces are up against minefields, anti-tank ditches and other obstacles, as well as layered defensive lines reportedly up to 20km deep in some places as they attempt to dislodge Russian occupiers.
The United Kingdom's Defence Ministry said on Tuesday the Kremlin's forces have "refined (their) tactics aimed at slowing Ukrainian armoured counteroffensive operations in southern Ukraine".
Russia has placed emphasis on using anti-tank mines to slow the onslaught, the assessment said, leaving the attackers at the mercy of Russian drones, helicopters and artillery.
"Although Russia has achieved some success with this approach in the early stages of Ukraine's counteroffensive, its forces continue to suffer from key weaknesses, especially overstretched units and a shortage of artillery munitions," the UK assessment said.
Russian shelling of Pervomaiskyi, a city in Ukraine's northeastern Kharkiv region, wounded 43 civilians, Kharkiv governor Oleh Syniehubov said on Tuesday.
Among the wounded were 12 children, including two babies, according to officials.
Oleksandr Lysenko, mayor of the city of Sumy in northeastern Ukraine, said that three people were killed and 21 others were wounded in a Russian drone strike on Monday that damaged two apartment buildings.
Ukrainian President Volodymyr Zelenskiy said the attack also damaged the regional headquarters of the Security Service of Ukraine, the country's main intelligence agency.
He argued that the country needs more air defence systems to help fend off Russian raids.
In all, Ukraine's presidential office said, at least seven Ukrainian civilians were killed and 35 others injured in the fighting over the previous 24 hours.
Putin referred to the recent mercenary rebellion that rattled the Kremlin during a video call on Tuesday with leaders of the countries of the Shanghai Cooperation Organisation, or SCO.
Putin said that "Russian political circles, the entire society have shown unity and responsibility for the fate of the motherland by putting up a united front against the attempted mutiny".
He thanked the SCO members for what he described as their support during the uprising.
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