Air defenses have been activated, but several drones have managed to reach energy giant Gazprom's oil facility in southeast Moscow, Mayor Sergei Sobyanin wrote on social media. Footage shows huge flames shooting from buildings there and black smoke billowing.
Several other videos distributed and verified by independent Russian media sources show high-rise buildings that have been hit and started to burn.
In Zhukovsky, southeast of Moscow, an apartment building with more than 20 floors is on fire. The entire building has been evacuated and images show flames on some of the highest floors.
Many are reported shot down
Earlier in the morning, Mayor Sobyanin said that at least 50 drones had been shot down as they flew towards the Russian capital. Russia's Defense Ministry later announced that more than 550 drones had been shot down over the country. Up to 200 of them were reportedly heading towards Moscow.
It is the second time this week that the oil refinery has been attacked. The most recent damage was caused by drone strikes on Tuesday. Ukraine has targeted Moscow more recently.
Local authorities are reporting material damage to, among other things, a shopping center and residential buildings after last night's attacks.
In the Rostov region near the border with eastern Ukraine, one person was reportedly killed in an attack.
"Justified"
"This is a completely justified response to Russian attacks on our cities and communities," Ukrainian President Volodymyr Zelenskyy wrote on social media.
In the Ukrainian capital Kyiv, there were also reports of rocket attacks and explosions during the night. By morning it was not yet clear whether anyone had been killed. Earlier this week, several people were killed in similar Russian attacks.
Attacks and explosions are reported in more Ukrainian regions.
