Floyd Mayweather -- Rocking $25k Mouthpiece ... With Real $100 Bills Inside

Floyd Mayweather is so MONEY -- his mouthpieces are stuffed with REAL $100 BILLS ... TMZ Sports has learned.

This is no joke ... we've learned Floyd pays roughly $25,000-a-pop to get custom grill-protectors from NYC-based dentist Dr. Lee Gause -- one of the most famous mouthpiece makers in pro sports.

So why the high price tag?

Well, the fact Floyd often customizes his guards with things like gold flakes, diamonds and real $100 bills (sealed inside the mouthguard) ... ups the price from the regular pieces.

Plus, Dr. Guase often flies out to Vegas to customize the fit for "Money" before a fight -- and Floyd says Gause's guards help him breathe better than other mouthpieces.