"The President of the Republic considers that the current situation in eastern Ukraine still does not allow for the delivery of the first" warship, Hollande's office said in a statement.
"He therefore decided to delay until further notice" the decision on whether to grant the export licence needed to deliver the ship to Russia, the statement added.
Russia has reportedly warned Paris of "serious" consequences unless France delivers the first of two Mistral-class helicopter carriers on order by the end of November.
The first of the two assault ships was supposed to be delivered earlier this month, according to the original deal signed in 2011.
But amid the Ukraine crisis and the rapid decline in the West's relations with Russia, France has come under intense pressure from its allies, particularly the United States, and in September postponed the delivery.
Later on Tuesday Russia said it does not plan to file a claim against France after it delayed the delivery of a hi-tech warship over the Ukraine crisis, deputy defence minister Yury Borisov said Tuesday.
"We'll wait patiently... So far we are not filing a claim anywhere," Borisov told RIA Novosti news agency after French President Francois Hollande said the time was not right to deliver the helicopter carrier.