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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. Plain Language Summary: In the next generation of geothermal development, massive volumes of fluid are injected underground to either create a potential geothermal reservoir or enhance fluid flow. In that process, water migration can be tracked by small earthquakes that are rarely felt by humans. The region of small earthquakes can be regarded as an active geothermal reservoir. Knowing the reservoir's shape may improve the assessment and design of the energy extraction system. However, it is difficult to forecast the shape of a possible geothermal reservoir prior to fluid injection. This study investigated the temporal variations in the shape of the region of small earthquakes caused by fluid injection using the data from the geothermal project at Basel, Switzerland. We found that the region's shape is correlated to the local stress when the reservoir hosted various existing fractures. Thus, the geothermal reservoir shape can be forecasted in advance using knowledge of the regional stress, which may allow for better assessment of geothermal development. Key Points: Microseismic cloud shape is correlated to in situ stress ratio and the permeability tensorMicroseismic cloud growth is mainly controlled by in situ stress if there is sufficient variation in existing fracture orientationMicroseismic cloud shape can be forecasted macroscopically with the in situ stress ratio, for use in designing an energy extraction system [ABSTRACT FROM AUTHOR]