Ukraine has not claimed Russian involvement, but Mr Zelensky told the World Economic Forum in Davos the tragedy was a consequence of the war.
Interior Minister Denys Monastyrsky died, alongside several colleagues.
Mr Zelensky also used his video address to urge allies to quickly send more weapons before new Russian offensives.
"The time the free world uses to think is used by the terrorist state to kill," he explained. The remark was interpreted as a request for Germany to hurry along a delivery of its much-coveted Leopard tanks.
Berlin has reportedly been unwilling to send the vehicles unless the US commits to providing its own Abrams battle tanks. The UK recently pledged to send a number of its own tanks to Kyiv.
The head of the Nato military alliance said at Davos on Wednesday that Ukraine could expect to receive "more support, more advanced support, heavier weapons and more modern weapons".
Jens Stoltenberg said Nato's member states would meet on Friday to discuss what military equipment could be sent to Kyiv.
Wednesday's helicopter crash occurred near a nursery in Brovary, outside Kyiv, at around 08:30 local time (06:30 GMT). One of the 14 who died was a child.
Mr Monastyrsky, 42, was one of President Zelensky's longest serving political advisers. He is the highest-profile Ukrainian casualty since the war began.
His 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.
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.
The deputy head of Ukraine's presidential office said Mr Monastyrsky had been travelling to a war "hot spot". The head of police in Kharkiv added that the ministerial team had been on its way to meet him.
There is no indication the crash was anything other than an accident.
But the SBU state security service said it was considering several possible causes - including sabotage, a technical malfunction or breach of flight rules.
Key officials are often flown by helicopter across Ukraine at tree-level to avoid detection, 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 remains of the helicopter were visible outside a residential building in Brovary
Other officials who died in the crash included first deputy minister Yevhen Yenin and state secretary Yuriy Lubkovych, as well as Tetiana Shutiak, an aide to Mr Monastyrsky.
Following the disaster, Ihor Klymenko - the head of Ukraine's national police force - was appointed acting interior minister.
A friend of the late minister, 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.
US President Joe Biden labelled the crash a "heartbreaking tragedy".
Interior Minister Denys Monastyrsky and first deputy minister Yevhen Yenin
Parents were bringing their children to the kindergarten before going to work when the helicopter came down nearby.
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.
Witnesses in Kyiv agreed with President Zelensky that the 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.
Other witnesses said the pilot had tried to avoid high-rise buildings before the crash, and instead went down near the kindergarten.
"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.
One resident, Dmytro, described jumping over a fence to help get children out. He said he picked up one girl whose father did not recognise her as her face was covered in blood.
The incident came four days Ukraine was hit by one of the deadliest attacks on civilians since the start of the war.
A Russian missile hit a block of flats in the central city of Dnipro, killing 45 people, including six children.