Multi-stage hydraulic fracturing of horizontal wells is the main stimulation method in recovering gas from tight shale gas reservoirs, and stage spacing determination is one of the key issues in fracturing design. The initiation and propagation of hydraulic fractures will cause stress redistribution and may activate natural fractures in the reservoir. Due to the limitation of the analytical method in calculation of induced stresses, we propose a numerical method, which incorporates the interaction of hydraulic fractures and the wellbore, and analyzes the stress distribution in the reservoir under different stage spacing. Simulation results indicate the following: (1) The induced stress was overestimated from the analytical method because it did not take into account the interaction between hydraulic fractures and the horizontal wellbore. (2) The hydraulic fracture had a considerable effect on the redistribution of stresses in the direction of the horizontal wellbore in the reservoir. The stress in the direction perpendicular to the horizontal wellbore after hydraulic fracturing had a minor change compared with the original in situ stress. (3) Stress interferences among fractures were greatly connected with the stage spacing and the distance from the wellbore. When the fracture length was 200 m, and the stage spacing was 50 m, the stress redistribution due to stage fracturing may divert the original stress pattern, which might activate natural fractures so as to generate a complex fracture network.