In a western district of Kyiv, drone debris fell into a multi-storey residential building, igniting fires in several flats.
There were initially no reports of casualties or damages.
The general director of the children’s hospital estimated the damage caused by the missile strike to medical equipment alone to be almost €9 million.
Irish premier Simon Harris has called a Russian missile strike on a major children’s hospital in the Ukrainian capital a “despicable act.”
The visit is Mr Blinken’s fourth visit to Kiev since the Russian invasion of Ukraine in February 2022.
The video suggests that military personnel were present in the hospitals, it said.
According to the Ukrainian Air Force, two ballistic missiles were fired at the city of millions from the Russian-controlled Crimea Peninsula.
