According to new legal docs obtained by TMZ … the music mogul -- who co-founded Roc-A-Fella with Jay-Z and Kareem Burke -- will have his 33.3 percent interest in the company sold off by the U.S. Marshal at a public auction on August 29 in Manhattan.

The docs say bidders will have to first register to appear at the auction by sending an email to attorney Christopher Brown.

Brown, as you may know, represents film director Josh Webber, who secured an $800K-plus civil judgment against Dash for copyright infringement and defamation two years ago.

Webber and Muddy Water Pictures produced "Dear Frank" and filed suit against Dash after claiming he went around and told people he owned the rights to the movie even after he was dropped from the project.

The court docs specify the purpose of the auction is to collect on the judgment. The docs also note Jay Z's album "Reasonable Doubt" is the biggest asset Roc-A-Fella owns.

At auction, the minimum bid for Dash's shares cannot be less than $1.2 million.

What's more ... the purchaser must be able to plunk down a deposit of 20 percent of the minimum bid -- $240,000 -- at the time of the sale.