Many-body localization is a unique physical phenomenon driven by interactions and disorder for which a quantum system can evade thermalization. Although the existence of a many-body localized phase is now well established in one-dimensional systems, its fate in higher dimensions is an open question. We present evidence for the occurrence of a transition to a many-body localized regime in a two-dimensional quantum dimer model with interactions and disorder. Our analysis is based on the results of large-scale simulations for static and dynamical properties of a consequent number of observables. Our results pave the way for a generic understanding of occurrence of a many-body localization transition in a dimension larger than one and highlight the unusual quantum dynamics that can be present in constrained systems.