That I am aware of, there is no official template
If there was, it'd be in The Book of Vile Darkness, or else one of the Fiend Folios. I'm sad to say that I don't believe there's a template that mirrors Saint in terms of flavor or mechanics.
But...
I can propose some adjustments for you. Try doing this to the Saint template:
Requirements: Swap the requirement for a Good alignment with a requirement for an Evil one. Swap the prerequisite Exalted feats for Vile feats, and require a great act of evil in the name of a dark god (personal suggestion: a sacrifice of good-aligned sapient beings equal to double the character's hit dice).
Numerical Bonuses: Swap all instances of "perfection" bonuses with "profane" bonuses in the same areas. You can probably leave the energy resistance alone.
Spell-Like Abilities: Check and see which of the SLAs are distinctly "good" and replace them with evil ones. Some of them can probably stay, however, so don't go too crazy here.
Everything else, if I remember correctly, can remain the same.
Prestige Classes
There's a couple of prestige classes that might be useful to you if the villain in question is a fiend (an evil-aligned outsider) - namely, Fiend of Blasphemy and Fiend of Corruption, both of which can be found in the various Fiend Folios. These prestige classes give powers that help the fiend to corrupt, debase, and destroy souls in the names of greater patrons (or just Evil Itsownself) and could be very useful in your endeavor.
You can go up to 18 by buying, and then add your racial bonus.
from d20pfsrd
No score can be reduced below 7 or raised above 18 using [the purchase method]. See Table: Ability Score Costs for the costs of each score. After all the points are spent, apply any racial modifiers the character might have.
Best Answer
There is no official equivalent in 5e.
However, a barbarian who doesn't own anything can still be a viable combatant. As barbarians can add their Con bonus to their AC when not wearing armor and also halve most of the damage they take, you really don't need the AC bonus that the Vow of Poverty feat provides. Remember that in 5e, everyone's AC is lower than the equivalent creature in 3.5e. Some races, such as the lizardfolk or tortle, provide an alternative unarmored AC that could help, especially in the early levels.
In order to deal damage on par with a barbarian who does own things, you could either take the Tavern Brawler feat or choose a race with natural weapons (lizardfolk, perhaps?) to increase your unarmed damage. Alternatively, or additionally, you could take the Martial Adept feat and choose disarming strike in order to steal the weapons from opponents. Borrowing is not the same as owning, after all.
You will run into trouble by never owning a magic weapon to use against creatures immune or resistant to non-magical attacks. This can be dealt with by any spellcaster in the party casting Magic Weapon or Elemental Weapon on an improvised or stolen weapon you pick up.