We compared elastic-rock heterogeneity measured by borehole logging to the occurrence of seismic events caused by hydraulic fracturing of the corresponding rock sections. Our observations made from two hydraulic fracturing case studies suggest that elastic-rock heterogeneity controls the occurrence of fluid-injection-induced seismicity. The seismic events occurred preferentially in rock sections characterized by low Poisson’s ratio and high Young’s modulus. Based on analytic solutions of stress fluctuations in elastically heterogeneous media in equilibrium to a homogeneous far-field stress, we quantified the relation between elastic-rock heterogeneity and stress changes leading to fracture opening and reactivation in two end member models of 1D and 3D heterogeneity. We found that significant fluctuations of rock stress originated from elastic rock heterogeneity. Moreover, we found that stress changes leading to fracture opening and reactivation in rocks undergo scale invariance spatial fluctuations. This gave a possible physical explanation for the observed scale invariance of seismogenic processes. We analyzed the physical meaning of a heterogeneity index of rocks, which indicated rock sections of high Young’s modulus and low Poisson’s ratio. We found that this index can be used to identify rock sections of high differential stress. In addition, our results suggest that it is related to the occurrence probability of brittle rock failure during hydraulic fracturing. Nevertheless, we found that fluctuations of Poisson’s ratio showed an even stronger correlation to critical stress changes which resulted in opening and reactivation of fractures in rocks. We obtained an analytic solution of stress fluctuations in vertical transverse isotropic layers such as shale deposits and applied it to a hydraulic fracturing case study of a shale gas reservoir. Also in this case, we observed strong relations between seismicity and fluctuations of stress in space.