Arnault, the boss of the luxury conglomerate LVMH, insists his move is not aimed at avoiding high taxes about to be imposed on the wealthy by France's new Socialist government.
"Bernard Arnault has no other choice, given the extreme vulgarity and the violence of the headline... but to sue Libération," he said in a statement that said he was suing the left-wing daily for libel.
The headline, superimposed on a photo of the smiling LVMH boss carrying a red suitcase, is a play on a comment by ex-president Nicolas Sarkozy, who publicly muttered "Casse-toi, pov' con" ("Get lost, you poor idiot") at a man who refused to shake his hand.
The words became a taunt used by Sarkozy's left-wing critics.
Arnault, the world's fourth-richest man whose fortune Forbes magazine estimates at $41 billion, was close to Sarkozy.
He rejected criticism that he was being anti-patriotic on Sunday, insisting he was not becoming a tax exile, despite seeking Belgian nationality as crisis-hit France moves to impose a 75-percent tax on top earners.
"I am and will remain a tax resident in France and in this regard I will, like all French people, fulfil my fiscal obligations," he told AFP, adding that the bid for dual nationality was "linked to personal reasons".
Following the election of previous Socialist president Francois Mitterrand in 1981, Arnault lived in the United States for three years, returning to France after the Socialists switched to a more conservative economic course.
In a televised interview Sunday evening, President François Hollande, also a Socialist, said Arnault "must weigh up what it means to seek another nationality because we are proud to be French".
"One has to appeal to patriotism during this period," he said. Arnault's move has been widely condemned by French political parties on both the left and the far-right right as treacherous.
But François Fillon, who was prime minister under Sarkozy, denounced "stupid decisions" on the part of the current government which lead to "terrible results".
British Prime Minister David Cameron triggered a war of words with France in June by vowing to "roll out the red carpet" for French firms if Hollande implemented the new tax rate.