We propose a device for subwavelength optical imaging based on a metal-dielectric multilayer hyperlens designed in such a way that only large-wavevector (evanescent) waves are transmitted while all propagating (small-wavevector) waves from the object area are blocked by the hyper-lens. We numerically demonstrate that as the result of such filtering, the image plane only contains scattered light from subwavelength features of the objects and is completely free from background illumination. Similar in spirit to conventional dark-field microscopy, the proposed dark-field hyperlens is shown to enhance the subwavelength image contrast by more than two orders of magnitude. These findings are essential for optical imaging of weakly scattering subwavelength objects, such as real-time dynamic nanoscopy of label-free biological objects.