All drones heading to Moscow are said to have been shot down, but debris from one of the drones is reported to have landed on a major road in the capital area, according to The Kyiv Independent. No personal injuries have been reported.
Several Russian airports, including four around Moscow, stopped traffic due to the drone rain. Even in Volgograd and Nizhny Novgorod, air traffic was affected, writes news agency AFP.
According to Russian statements, more than 100 Ukrainian drones were sent to Russia during the night.
The relatively rare attacks come just days before the major military parade in Moscow on Friday's so-called Victory Day, when Russia celebrates the end of World War II.
Ukraine has not commented on last night's alleged drone attack.