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Not a charm but would be able to use Mind Blank to prevent it. The wording of mind blank is 

"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."

Due to the fact that Hold Monster is a Wisdom based save, that would suggest that the way that it works is an influence on the mind and therefore blocked by the mind blank. However, you would no give creatures that have advantage against charm effects the advantage, if that makes sense. 

Going by RAW, no it would not be able to. Mind Blank says nothing about it.

Wisdom, Intelligence and Charisma are often used as abilities for saving throws against general magical effects anyways, not just ones that affect the mind. So this spell being a Wisdom save suggests nothing of the sort. In fact if you ask me, neither this spell nor hold person even touch the mind, instead making use of magical force to hold the body in place. Thus the creature isn't really paralyzed at all, just so thoroughly restrained they might as well be.

 If it were magical force, it would be transmutation or abjuration, maybe even evocation if you're completely mad (they made wall of force evocation, after all.) There also wouldn't be target-based requirements (e.g. hold monster can't affect undead, hold person only affects humanoids). It's your table, but I'd say it counts as something mind-affecting, and thus would be blocked by "The spell even foils wish spells and spells or effects of similar power used to affect the target’s mind." Technically, it only works on thing of similar power to wish, but that's as dumb as a counterspell or globe of invulnerability that only works on spells of exactly 9th level.

I'm in the camp of "hold spells aren't affected by mind blank", but I do respect the opposite argument's logic.  Here's my counter:

The PHB describes the school of enchantment as "spells [which] affect the minds of others, influencing or controlling their behavior."  That seems pretty condemning, but it also says: "The schools of magic help describe spells; they have no rules of their own, although some rules refer to the schools."  I argue the hold spells are only classified as enchantments due to their ability to control the target's behavior by way of paralysis, which is a physical condition rather than a charm or something like the command spell.  In contrast, mind blank is very geared towards protection against emotional and intellectual manipulation or detection - like the charmed condition or the command spell.  It even specifies protection against a school of magic within its text - divination - but says nothing about protection from enchantments.

As for Wisdom saving throws, the DMG suggests that they be used for "resisting effects that charm, frighten, or otherwise assault your willpower."  The only relevance for hold spells is an assault on willpower; you could certainly argue that to be an affect on the target's mind, but considering the text of the spells in question I'd call it a stretch.

tl;dr -  the only direct correlation between hold spells and mind blank is the former's classification as enchantment spells, which by RAW is a descriptive tag against which mind blank specifically omits any protection.

I don't totally get it either. 
It doesn't work on undead but does work on constructs, elementals, and fiends. 
Undead are basically dark-magic constructs.
If it only worked on organic creatures or ones with actual minds, it wouldn't work on constructs.
I can understand it not working on ghost/spirit types, since their body is not physical at all.
But if it works on living flame essence and demons made out of evil-stuff it oughta work on skellies and zombos too. 

Banishment is just a very good spell. Also, if a creature is not native to your plane and as long as you keep concentration for the duration (a minute) the creature is unable to return, completely “banishing” it.