Commissioned in 2011, the 1.2 billion euro deal has attracted huge criticism after Russia was accused by Western nations, including France, of supporting separatist rebels in eastern Ukraine and even making military "incursions" into the Ukrainian territory.
However, France had until now resisted pressure to halt the delivery.
After a meeting of the French defense committee on Wednesday, Paris announced that the deliveries would not yet take place given the current unrest in eastern Ukraine.
"The President of the Republic declared that, despite the prospect of a ceasefire which still remains to be confirmed and implemented, the conditions for France to deliver the first warship are not to date in place," a statement from the office of French President Francois Hollande read.
France agreed in 2011 to build and sell the two advanced helicopter assault ships to Russia with the first scheduled for delivery in October or November and the second in 2015.
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