Cosmic voids are an important probe of large-scale structure that can constrain cosmological parameters and test cosmological models. We present a new paradigm for void studies: void detection in weak lensing convergence maps. This approach identifies objects that relate directly to our theoretical understanding of voids as underdensities in the total matter field and presents several advantages compared to the customary method of finding voids in the galaxy distribution. We exemplify this approach by identifying voids using the weak lensing peaks as tracers of the large-scale structure. We find self-similarity in the void abundance across a range of peak signal-to-noise selection thresholds. The voids obtained via this approach give a tangential shear signal up to $sim40$ times larger than voids identified in the galaxy distribution.