Kyrylo Tymoshenko, an aide to President Volodymyr Zelenskyy, said two buildings were damaged in Kyiv and a nearby suburban home was hit.
Officials said between 10 and 13 Shahed drones were shot down by air defences, and the damage appeared to be limited.
Mr Tymoshenko, however, warned that "the danger is not over yet" and told people to stay in shelters.
Ukraine's air force said the kamikaze drones were launched by Russia from east of the Sea of Azov.
"Today, the Ukrainian air defence took the terrorists down a peg," the Defence Ministry said.
Iran last month admitted supplying drones to Russia but claimed it was done before the war in Ukraine.
Britain on Tuesday accused Iran and Russia of making a "sordid deal" as it announced new sanctions against both countries.
The drone strikes came shortly after Mr Zelenskyy raised the alarm about unexploded mines and ordnance after 10 months of fighting.
In an address to New Zealand's parliament, he reported significant damage to Ukraine's rivers and forests and said 174,000 square kilometres of land were contaminated with explosives.
"The destroyed economy and infrastructure can be rebuilt. It takes years. But you cannot rebuild destroyed nature," he said.
"There is no real peace where any child can die from a hidden Russian anti-personnel mine. There is no real peace where the consequences of war in the form of poisoned groundwater can destroy normal life in several countries."
The Ukrainian military's general staff separately reported missile strikes in the Kharkiv, Donetsk and Zaporizhzhia regions over the past day.
The military claimed to have destroyed another four Russian tanks and repelled attacks in Kharkiv, Donetsk and Luhansk.