Interior Minister Denys Monastyrsky, 42, died alongside his first deputy minister and state secretary.
Fourteen people died when the helicopter came down in Brovary around 08:30 local time (06:30 GMT), including one child, authorities said.
There is no indication the crash was anything other than an accident.
But the SBU state security service said it was following several possible causes for the crash, which included sabotage as well as a technical malfunction or breach of flight rules.
The State Emergency Service had previously stated that up to 18 people were killed but later revised the death toll from the crash, saying 14 had died.
Mr Monastyrsky, who was one of President Volodymyr Zelensky’s longest serving political advisers, is the highest profile Ukrainian casualty since the war began.
The deputy head of Ukraine’s presidential office, Kyrylo Tymoshenko, said the minister had been travelling to a war “hot spot” when his helicopter went down.
The head of police in the north-eastern city of Kharkiv, Volodymyr Tymoshko, said the ministerial team were on their way to meet him there and he had spoken to them only yesterday.
The minister’s death cuts to the heart of the government in Kyiv as the interior ministry has the vital task of maintaining security and running the police during the war.
President Zelensky has spoken of a terrible tragedy that claimed the lives of “true patriots”.
The head of Ukraine’s national police force, Ihor Klymenko, has been appointed acting interior minister following Mr Monastyrsky’s death.
Witnesses in Kyiv said Russia’s war was to blame for the disaster.
“It was very foggy and there was no electricity, and when there’s no electricity there are no lights on the buildings,” local resident Volodymyr Yermelenko told the BBC.
Key officials are flown by helicopter across Ukraine at tree-level, but that comes with risks.
All that was recognisable of the helicopter was a door panel and one of its rotors which landed on the roof of a car. Next to it were three bodies covered in foil blankets.
The main kindergarten building was left badly damaged by the crash.
The 42-year-old interior minister was a prominent member of President Volodymy Zelensky’s cabinet.
He was a recognisable face for Ukrainians throughout the war, updating the public on casualties caused by Russian missile strikes since Ukraine was invaded in February 2022.
Ukrainian officials said those on board the helicopter included six ministry officials and three crew.
First deputy minister Yevhen Yenin died along with state secretary Yurii Lubkovich, whose task was to organise the work of the ministry.
Before he moved to the interior ministry, Mr Yenin helped represent Ukraine’s government abroad.
Mr Tymoshenko said the interior ministry’s work would not be affected by the loss of its leaders, but government colleagues were visibly shocked as they reacted on national TV.
A friend of the late minister’s, MP Mariia Mezentseva, said it was a tragedy for everyone as the ministry had a significant role in Ukraine’s response to the invasion.
“He responded 24/7 to his colleagues, friends and family. He was very close to President Zelensky from day one of his presidential campaign,” she told the BBC.
National police chief Ihor Klymenko wrote on Facebook that the helicopter belonged to Ukraine’s state emergency service, while other officials said it appeared to a be a French Super Puma aircraft.
Parents were bringing their children to the kindergarten before going to work when the helicopter came down.
“The pain is unspeakable,” the president said. “The helicopter fell on the territory of one of the kindergartens.”
Many of the casualties were on the ground. As well as the child that was killed, 11 of the 25 injured on the ground were youngsters. According to state emergency services officials, one child is missing.
Witnesses said the pilot had tried to avoid high-rise buildings before the crash, and instead went down near the kindergarten.
One local woman told the BBC that she had seen a terrible flash as the helicopter circled above her home. The pilot had clearly tried to avoid her 10-storey block of flats and chose to go down closer to the smaller building, she said.
“Parents were running, screaming. There was panic,” said local volunteer Lidiya. Emergency services and residents rushed to evacuate the children as fire spread through the nursery building.
Resident Dmytro described jumping over a fence to help get children out. One girl he picked up was called Polina, but when her father ran in calling her name he did not recognise her as her face was covered in blood.
Tetiana Shutiak, an aide to Mr Monastyrskyi, also died in the crash.
Interior ministry adviser Anton Herashchenko said the three men were friends and statesmen who had worked to make Ukraine stronger.
“We will always remember you. Your families will be cared for,” he said on Facebook.
Ms Mezentseva said she had initially thought that the disaster was fake news: “But unfortunately it’s true.”
It was only four days ago that Ukraine was hit by one of the worst attacks since the start of the war in which 45 civilians were killed.
A Russian missile hit a block of flats in the central city of Dnipro killing 45 people, including six children.
President Zelensky was due to address the World Economic Forum in Davos by video link later on Wednesday. Ukraine has appealed to the West to provide tanks to help respond to any expected new Russian offensive.
A decision is likely to be made later this week when Western allies discuss the war at Ramstein air base in Germany.