Minimalism is one of those terms people like me love to throw around because it conveys an idea, rather than a strict set of rules or traits, and so is very hard to technically misuse.
Let's take a look at some of the different approaches to minimalism in craft beer label art. First, the Goose Island Belgian Style series:
In this case, minimalism means a ton of negative space, limited color and form, and a focus on understated, text-driven design. It gives it a very upper-class feel. Other breweries that use variations on this are Southampton and Allagash, both for higher-end specialty beer lines.
North Peak is one of the many breweries that use a nostalgia-infused minimalism (that I generally love) in their branding.
as Don Draper would put it, "a place where we ache to go again."
Minimalism can be modern, too, though. Portland, OR's Laurelwood Brewery has a fairly minimal look for its Green Elephant IPA:
Just Beer's Flip Flop follows a similar strategy, with a less hipster twist.
Lastly, let's look at two different tacks on the idea. First, the Captain Lawrence limited-edition sour:
Compare to the standard logo:
Finally, the Odell Deconstruction is a different type of minimalism:
referencing Jacques Derrida, I'm on board. And in this case, the "minimalist" element is not simplicity of form but of subject matter. It's a barrel with stenciled lettering and hand-drawn red markup. There's almost no negative space or simple monochrome shapes, but the idea of the label plays against your expectations and maintains focus on a basic staple. In this case, the label art idea appropriately plays on the philosophy reference that named and informed the creation of the beer.
As you can see, minimalism is a wide and varied field for breweries to inhabit with all kinds of different labels. The point of all this was to demonstrate that, for as much as I love the intricacies of Left Hand or the over-the-top color cacophony of Terrapin, a disciplined focus on basic elements can lead to very effective art and design.