His net worth has soared by $55.3bn (£44.44bn) since January to $192bn, after a rise in the value of his electric car company Tesla.
Mr Arnault’s fortune has fallen by $24.5bn to $187bn, per Bloomberg’s Billionaires Index.
He is followed by Jeff Bezos and Bill Gates in third and fourth positions.
Mr Arnault, 74, had overtaken Mr Musk, 51, on the the rich list in December when shares in LVMH jumped as demand for luxury goods rebounded.
At the same, shares in Tesla – the company from which Mr Musk derives most of his wealth – fell sharply amid concerns that his takeover of the social media platform Twitter was affecting his leadership.
However, Tesla shares have bounced back by almost 92% since the start of this year as investor nerves have eased and Mr Musk has announced his replacement as Twitter chief executive.
His visit to China this week to discuss Tesla has also sparked excitement, while the car firm is benefiting from the rise in interest in artificial intelligence.
By contrast, LVMH – which owns brands including Louis Vuitton and Christian Dior – has gone into reverse.
After hitting a record high in April, its shares have fallen sharply and are down 16% since the start of the year.
Mr Arnault, who co-founded the luxury goods giant in 1987, owns a majority stake in the business, which is Europe’s most valuable firm.
In January, the Frenchman appointed his daughter Delphine Arnault, 47, as head of his fashion house Dior as part of a shake-up at LVMH.
All five of Mr Arnault’s children hold management positions at brands in the group.
According to Bloomberg, Amazon founder Jeff Bezos is the world’s third richest person with a fortune of $146bn. Mr Gates, who co-founded Microsoft, is worth $126bn.