Cells assemble a variety of bundled actomyosin structures in the cytoskeleton for activities such as cell-shape regulation, force production, and cytokinesis. Although these linear structures exhibit varied architecture, two common organizational themes are a punctate distribution of myosin II and distinct patterns of actin polarity. The mechanisms that cells use to assemble and maintain these organizational features are poorly understood. To study these, we reconstituted actomyosin bundles in vitro that contained only actin filaments and myosin II. Upon addition of ATP, the bundles contracted and the uniformly distributed myosin spontaneously reorganized into discrete clusters. We developed a mathematical model in which the motion of myosin II filaments is governed by the polarities of the actin filaments with which they interact. The model showed that the assembly of myosins into clusters is driven by their tendency to migrate to locations with zero net actin filament polarity. With no fitting parameters, the predicted distribution of myosin cluster separations was in close agreement with our experiments, including a -3/2 power law decay for intermediate length scales. Thus, without an organizing template or accessory proteins, a minimal bundle of actin and myosin has the inherent capacity to self-organize into a heterogeneous banded structure.