From the Mind Blank spell's description:
The spell even foils wish spells and spells or effects of similar power used to affect the target's mind or to gain information about the target.
Hence, a creature under the effects of Mind Blank should intuitively be immune to Madness from p. 259 of the DMG.
As answered by "Does the Mind Blank spell prevent the target from being frightened?", however, unless an effect explicitly targets the mind (as Feeblemind does) or other points mentioned in the spell's description, it seems like Mind Blank would offer no protection against the effect (e.g the aforementioned question answers that Mind Blank does not protect against being frightened). Certain types of madness lie within this category, such as:
31-40: The character becomes frightened and must use his or her action and movement each round to flee from the source of the fear.
From p. 39 of the Curse of Strahd adventure, however:
The Mad Mage has forgotten his name and the world whence he came. In fact, he doesn't remember anything that happened before the madness... Under normal circumstances, a greater restoration spell cast on the Mad Mage would restore his wits and end the madness... But in this case, the Mad Mage has cast a mind blank spell on himself. As long as that spell remains in effect, his sanity can't be restored by any spell.
There are two interpretations of the above example:
- A creature's current sanity/madness level is an aspect of the mind protected by Mind Blank. Therefore although certain effects of madness may not explicitly target the mind, so long as it is a type of madness it is protected against by Mind Blank.
- Mind Blank does not protect against all types of madness, but the above example happens to be one of which that is protected since the text explicitly details its interaction with Mind Blank.
As the above is the only example I know of where madness and Mind Blank interact, I have very little data to go on.
Are there any other examples from published sources or rules I missed to help explain whether Mind Blank protects against all types of madness?