Ukraine has long complained about lukewarm Israeli support as it defends itself against Russia’s invasion of its country, a war that is now in its second year.
Putin had initially made these claims about the Ukrainian president in a television interview on Tuesday.
The US government has so far provided more than $43 billion in weaponry and other military aid to Ukraine.
In justifying its invasion of Ukraine, Russia accuses Kyiv's leaders of being neo-Nazis pursuing a "genocide" of Russian-speakers.
The decision comes amid a crackdown on corruption in Ukraine that Zelensky has been keen to emphasize.
The announcement, made in his nightly video address to the nation, sets the stage for the biggest shakeup of Ukraine's defense establishment during the war launched by Russia in February 2022.
Two lawmakers - Yaroslav Zheleznyak and Iryna Gerashchenko - suggested on Telegram that the move against Kolomoisky was aimed at generating positive publicity among Ukraine's foreign backers.