In total, nine people were injured in the strike on the day that peace talks were set to begin in Saudi Arabia between Kyiv and Washington.
Eight of these, including a child, were in the Moscow region, governor Andrei Vorobyov claimed.
Ukraine war latest: Peace talks set to begin
One of the injured was wounded on a highway in the Lipetsk region, according to a local governor.
Most of the 337 drones were said to have been shot down over the contested Kursk region across the border from Ukraine.
But 10 regions were targeted in total.
A further 91 drones were shot down over the Moscow region as mayor Sergei Sobyanin claimed over 70 drones targeted the Russian capital itself.
He also said the country’s air defences had repelled the strike on Tuesday.
The attack damaged seven apartment buildings in the area and left a number of cars burning in a car park elsewhere, according to Russian state news agencies RIA Novosti and Tass.
Flights were restricted in and out of six airports, and trains were temporarily suspended, according to local officials.
Other regions said to have been targeted included Belgorod, Bryansk and Voronezh on the border with Ukraine and those deeper inside Russia, such as Kaluga, Lipetsk, Nizhny Novgorod, Oryol and Ryazan.
There was no immediate comment from Ukrainian officials on the attack.
Meanwhile, Ukraine’s air force said overnight it shot down a ballistic missile and 79 drones launched by Russia.
Such back-and-forth attacks have been a near-nightly occurrence since Russia’s invasion in February 2022.
However, the scale of this Ukrainian attack seems to set it apart from past strikes.
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Peace talks set to begin
On Tuesday, a Ukrainian delegation is set to meet with America’s top diplomat in the Middle East to discuss ending the years-long war with Russia.
While President Volodymyr Zelenskyy was in the country, after meeting with Crown Prince Mohammed bin Salman he then left, leaving behind a team to meet with Marco Rubio and US officials.
It would mark the first official talks between the countries after a disastrous meeting in the White House that saw Mr Zelenskyy berated in front of the world’s media by President Donald Trump and vice president JD Vance.
Mr Zelenskyy had travelled to Washington to sign a critical minerals deal.
This week, Ukraine is expected to propose a ceasefire covering the Black Sea and long-range missile strikes, as well as a prisoner release, according to two senior Ukrainian sources.
The officials added that Kyiv was ready to sign the minerals deal.
