Rescue workers and medics dug through the rubble to look for survivors, though it was unclear how many were still trapped.
On Monday afternoon, Kyiv’s Mayor Vitali Klitschko said 16 people, including seven children, had been injured in the hospital strike.
He said the attacks across the city were among the worst Kyiv had faced since the beginning of the war, as he ordered flags to be flown at half-mast on Tuesday and cancelled entertainment events.
Following the strike, Ukrainian tennis player Elina Svitolina wore a black ribbon as a mark of respect when she played in the round of 16 at Wimbledon on Monday afternoon.
She fought back tears during her post-match interview, saying: “It wasn’t easy to focus today on the match.
“Since the morning it was difficult to read the news. To go on the court is extremely tough.”
The UN’s human rights monitoring mission in Ukraine has said civilian casualties have been mounting in recent months, as Russia renewed its air campaign.
A recent report said May was the deadliest month for civilian deaths in almost a year.
On Tuesday morning, the governor of the Rostov region in southern Russia said a fire had broken out at a powerplant after Ukraine launched “tens” of drones.