The statement provided no other details about the alleged offences.
The Irishman, 32, vigorously denied the claims after he was held by French police following an incident in a bar.
"Conor McGregor vigorously denies any accusations of misconduct. He has been interviewed and released," he told The New York Post through a spokesman.
His manager also came out swinging on his behalf.
"I am irate and putting out a warning loud and clear: Conor McGregor is not and will not be a target for those seeking to score a headline or a payday," Audie Attar said in an e-mail to The Post.
The Irishman, whose nickname is "Notorious" returned to the Octagon early this year after completing court-ordered community service for a bus of rival MMA fighters leaving Brooklyn's Barclays Center in 2018. He also faced a civil suit in Miami after his arrest for destroying a fan's cell phone.
He announced his third retirement from the sport in June.
The former Ultimate Fighting Championship star is vacationing on the French island with fiancee Dee Devlin and their two children.
He was held just hours before he was due to take part in a 130km water bike charity race from Corsica to Monaco as part of a joint campaign with Princess Charlene of Monaco to highlight water safety.
McGregor's arrest comes just days after the US anti-doping agency came to test him in Corsica despite the fact he has retired.
''What's going on here UFC," McGregor tweeted. "I've retired guys! But go on then, I'll allow them to test me. It's all natural baby!''