Conservative Prime Minister Dominique de Villepin announced the decision in an apparent bid to forestall further protests by unions and left-wing opponents who have attacked the 7 billion euro ($8.5 billion) EDF sale partly on nuclear safety grounds.
The government had planned to sell part of Areva in 2006 in a move expected to raise up to 3.6 billion euros ($4.4 billion).
"In a sector as strategic as the supply of fissile matter, enrichment and the treatment of nuclear waste, state control must supply the guarantees which are necessary to our citizens and our foreign clients," Villepin said.
"You will understand that under these conditions, the opening of Areva's capital is not part of my government's agenda," he said at a monthly news conference.