Physicist: The very short answer is no: darkness is not a wave. There are no waves in the dark for very much the same reason that there’s no surfing (or ocean waves) in Death Valley. Darkness, being an absence of electromagnetic waves (light) has nothing to do any waving.
If you define the speed of dark to be the speed at which you could find out about someone turning out the lights, it’s exactly the same as the speed of light: 671 million mph, or 2.99 x 108 m/s, or about 1 foot per nanosecond. For example, if the Sun were to suddenly go out (unlikely), then the darkness wouldn’t get to the Earth for a solid 8 minutes.
The somewhat longer answer (that sound like it undermines the short answer, but totally doesn’t) is that “darkness”, while not a wave itself, can be produced by light waves. Light waves, rather than merely being there or not can add and subtract from each other (at each tiny point in space).
So if you’re looking at a particular point in space there can be light waves present, but they may cancel each other out, creating a little dark patch. In this sense light has more in common with money than most “actual” things. You can have positive money (colloquially; “bones”) or you can have negative money or debt (vernacularly; “boned”), and it’s not unless you have neither, or equal amounts of both, that you’re exactly broke.
Light is similar. Correctly prepared light can produce doubly bright or completely dark regions. What’s really slick, is that these regions can move faster than light! There are a lot of effects like this that get a lot of people excited, but before you get too excited; don’t. It has to do with the difference between “phase velocity” and “group velocity”, but the basic idea is that these dark and light patches move faster than light in exactly the same way that the intersection of the blades of a pair of scissors move faster than either blade. There’s an old post that talks about one of the more exceptional examples of this.
Long story short: darkness isn’t a wave itself because it isn’t anything, if it has a speed it’s the same as light speed, and also light is profoundly weird stuff (and not to be taken lightly).
The ocean, desert, basket, and hypnotic pictures are from here, here, here, and here.