Several explosions were heard in the city on Monday, one week after a barrage of Russian strikes on Ukraine.
At least three explosions have been heard in the Ukrainian capital Kyiv, after air raid sirens went off.
Mayor Vitalii Klitschko said residential buildings in the central Shevchenkivskiy area have been damaged.
Andriy Yermak, head of President Zelensky’s office, said the attacks were from so-called kamikaze drones.
It comes a week after the capital was hit by several Russian missiles at rush hour, in a nationwide attack which left 19 dead.
The explosions happened at around 07:00 local time (04:00 GMT), said the BBC’s Paul Adams, who is in the city.
Writing on the Telegram social media site, Mr Klitschko said they were in the Shevchenkivskiy district, which was hit by several strikes last week.
He said rescuers were on site, and told residents to stay in air raid shelters.
Russian President Vladimir Putin said the strikes last week were in retaliation for the bombing of a key bridge linking Russia to occupied Crimea, which he blamed on Ukraine.
It was the first time during the war that the centre of Kyiv had been directly targeted.
Earlier this week, Mr Putin said there was no need for more large-scale strikes on Ukraine.
Most designated targets had been hit, he said, adding that it was not his aim to destroy the country.