In situ stress is an important factor affecting the permeability and hydraulic fracturing of a coal seam reservoir. In this study, the in situ stresses of 166 coalbed methane (CBM) wells in the Fanzhuang block of the southern Qinshui Basin, China, were tested using a hydraulic fracturing method. The correlation between the burial depth of No. 3 coal seam and in situ stress was established, and the influence of in situ stress on hydraulic fracture characteristics and reservoir permeability was analyzed. The Fanzhuang block was divided into five regions according to the burial depth, in situ stress characteristics, and lateral pressure coefficient. Considering the state of the in situ stress field, the horizontal principal stress difference coefficient, and the development characteristics of natural fractures (cleats) in the coal, hydraulic fractures in the five areas were predicted. Permeability increases exponentially with the porosity and decreases exponentially with in situ stress. Within the study area, the permeability of the well test had a negative exponential relationship with the lateral pressure coefficient, and turning points appeared at lambda approximate to 1.0 and 2.0. In the compression zone, permeability decreases with an increase in the stress anisotropy index; in contrast, in the extension zone, permeability increases with an increase in the stress anisotropy index. The results provide a theoretical basis for CBM development and hydraulic fracturing of CBM wells in the study area.