The shapechange spell question has raised a difference in opinion on whether or not the proficiency bonus is a class feature.
The crux of the issue is that shapechange allows the character to retain their class features in their new form. If the proficiency bonus is a class feature then the character can retain it, if it is not then they cannot. This has potential implications for determining proficiencies of the final form.
The game feature shapechange is most similar to is the druid's Wild Shape feature (they even include the same text block on character stats).
As a result any rules implications for shapechange or vice versa would likely also arise in relation to Wild Shape.
Is a character's proficiency bonus a class feature or not?
Best Answer
No, but you still keep that bonus for Wild Shape.
Each class has a section called Features, that lists all its class features. These include, for a Barbarian, Rage, Unarmored Defense, Reckless Attack, Danger Sense, etc. The Proficiency Bonus is not listed there.
Chapter 7 of the PHB describes it as
The character advancement table in PHB, pg16, shows your Proficiency Bonus regardless of class.
The Multi-Class chapter also lists Proficiency Bonus based on character level, not class levels.
It also does not list Proficiency Bonus under special rules for Class Features gained, as Marq points out.
Just for completeness's sake, monsters have Prof Bonuses too, although based on their CR and not Character Level. It is shown in the Monster Manual, pg.8, and on the DMG, pg. 274 (thanks to Slagmoth for the tip).
Keeping the proficiency bonus for Wild Shape
Despite not being a Class Feature, it still carries over on Wild Shape or Shapechange, as confirmed by lead rules designer Jeremy Crawford on Twitter. The ability/spell mentions you take your original proficiencies, and that includes this Proficiency Bonus.
(This also means the Proficiency Bonus doesn't have to be considered a class feature to be kept in Wild Shape.)