We identify the smallest discrete flavor symmetry and minimal field content that can simultaneously account for neutrino masses and the dark matter sector. Minimality is achieved with a $D_4$ symmetry by adding three right-handed neutrinos and two scalar doublets. Within this framework, tree-level and one-loop contributions yield the observed solar-atmospheric mass hierarchy and neutrino mixing angles. The inclusion of a third right-handed neutrino transforming as a $D_4$ singlet is essential to generate the reactor angle $\theta_{13}$. Furthermore, by including CP-violating phases, the model successfully accommodates both normal and inverted ordering scenarios. Spontaneous $D_4$ breaking leaves a residual $\mathbb{Z}_2$ symmetry that stabilizes the dark matter candidate, while the model admits viable regions of parameter space compatible with cosmological and direct-detection constraints.