Moore's lawyers have filed the demand at the Superior Court of California, claiming that Kutcher, now in US TV sitcom "Two And A Half Men", has amassed a fortune in shrewd investments since they married in 2005.
They split in November 2011 after allegations he cheated on her with a young starlet on their wedding anniversary.
The settlement case is unlikely to be heard before the end of the summer because the two mega-rich stars are so bitterly embroiled in financial wranglings.
The actress's lawyers argue she is entitled to reap the benefits as Kutcher made the investments on the advice of her friends in a case that could have far-reaching effects.
Spokesmen for both stars refused to comment.