Forecasting microseismic cloud shape as a proxy of stimulated rock volume may improve the design of an energy extraction system. The microseismic cloud created during hydraulic stimulation of geothermal reservoirs is known empirically to extend in the general direction of the maximum principal stress. However, this empirical relationship is often inconsistent with reported results, and the cloud growth process remains poorly understood. This study investigates microseismic cloud growth using data obtained from a hydraulic stimulation project in Basel, Switzerland, and explores its correlation with measured in situ stress. We applied principal component analysis to a time series of microseismicity for macroscopic characterization of microseismic cloud growth in two- and three-dimensional space. The microseismic cloud, in addition to extending in the general direction of maximum principal stress, expanded in the direction of intermediate principal stress. The orientation of the least microseismic cloud growth was stable and almost identical to the minimum principal stress direction. Further, microseismic cloud shape ratios showed good agreement when compared with in situ stress magnitude ratios. The permeability tensor estimated from microseismicity also provided a good correlation in terms of direction and magnitude with the microseismic cloud growth. We show that in situ stress plays a dominant role by controlling the permeability of each existing fracture in the reservoir fracture system. Consequently, microseismic cloud growth can be scaled by in situ stress as a first-order approximation if there is sufficient variation in the orientation of existing faults.