"This is about a capital increase of 2.9 billion euros (3.9 billion dollars) at the heart of his Belgian enterprise Pilinvest," Jennifer Vanderputten, spokeswoman for the Brussels prosecutor's office, was quoted by De Tijd.
"We are also investigating a possible address fraud," she added.
This reportedly relates to an apartment of Arnault's in a Brussels suburb.
Pilinvest is a holding company founded by Arnault in 1999. The company's capital rose to 368 million euros between 2005 and 2007, while the transaction under investigation took place in December 2011.
Official documents state that the transaction related to 4 million shares of a "non-listed company under French law," de Tijd wrote. No further financial statements were provided, despite a legal requirement.
The prosecutors want to know why, and under what circumstances, the money was transferred to Belgium, the newspaper wrote, adding that they were also investigating links to a Luxembourg holding company that Pilinvest had shares in.
Arnault caused a furore in his native France last year when it emerged that he was seeking citizenship in Belgium, which has a more friendly tax regime. He abandoned the bid earlier this year.
He is the world's 10th-richest person, with an estimated family net worth of 29 billion dollars, according to a survey by Forbes magazine.
Belgium has no wealth tax and its taxes on inheritances and capital gains are also lower than France's, a fact that has lured several French top earners across the border in recent years.