The 41-year old Swiss national threatened to publish photos and videos that an Italian accomplice secretly took when the former couple met at a Munich hotel, the newspaper said, citing Klatten's spokesman Joerg Appelhans.
Both men were arrested in Austria after Klatten informed prosecutors. Her ex-lover has been extradited to Germany where he's now in custody, the newspaper said.
Appelhans didn't immediately return a call seeking comment.
Klatten has a fortune valued at 7.8 billion euros and is married with three children, Bild reported.
