The head of Kyiv's military administration, Tymur Tkachenko, said three people had suffered shrapnel wounds.
Tkachenko said six city districts had been hit, with fires breaking out in various buildings, storage areas and cars and drone fragments falling to the ground in different parts of the city.
"The enemy attack is continuing," he wrote. "The defence forces are taking on enemy targets."
Ukraine's military issued warnings on the Telegram messaging app that the city could also be subject to a missile attack.
Reuters witnesses reported a series of loud explosions.
Kyiv Mayor Vitali Klitschko said emergency crews were at an apartment building in the central Shevchenkivskyi district, where falling drone fragments had triggered a fire on the top floor. Another fire was being tackled, also in the city centre.
Klitschko put the number of injured at two people in hospital.
On Tuesday night, Russian forces unleashed their largest drone attack on Ukraine since the start of the now 40-month-old war, with 728 drones targeting widely separated regions, including western Ukraine.
That attack took place hours after U.S. President Donald Trump pledged to send more defensive weapons to Kyiv and aimed unusually sharp criticism at Russian President Vladimir Putin.
(Reporting by Gleb Garanich and Ron Popeski; Editing by Sandra Maler and Christopher Cushing)

Servicemen carry the coffin of late Ukrainian serviceman Roman Oryshchenko during a farewell ceremony at the St. Mykhailivsky Cathedral in Kyiv, Ukraine, 09 July 2025, amid the ongoing Russian invasion. Roman Oryshchenko, 47, with callsign 'Orlyk', served in the 72nd Separate Mechanized Brigade, known as the 'Black Zaporozhians', and was killed in battle for Ukraine on 02 July 2025 on the Donetsk direction. Roman was a Maidan activist during the Revolution of Dignity in 2013-2014, one of the key creators of the Maidan Self-Defence, and an activist of Plast, the Ukrainian national scout organization. EPA/SERGEY DOLZHENKO