Supporting high data rate wireless connectivity among wearable devices in a dense indoor environment is challenging. This is primarily due to bandwidth scarcity when many users operate multiple devices simultaneously. The millimeter-wave (mmWave) band has the potential to address this bottleneck, thanks to more spectrum and less interference because of signal blockage at these frequencies. In this paper, we explain the potential and challenges associated with using mmWave for wearable networks. To provide a means for concrete analysis, we present a system model that admits easy analysis of dense, indoor mmWave wearable networks. We evaluate the performance of the system while considering the unique propagation features at mmWave frequencies, such as human body blockages and reflections from walls. One conclusion is that the non-isotropy of the surroundings relative to a reference user causes variations in system performance depending on the user location, body orientation, and density of the network. The impact of using antenna arrays is quantified through analytic closed-form expressions that incorporate antenna gain and directivity. It is shown that using directional antennas, positioning the transceiver devices appropriately, and orienting the human user body in certain directions depending on the user location result in gigabits-per-second achievable ergodic rates for mmWave wearable networks.