Refracturing, temporary plugging, and infilling well design play an important role in the development of reservoirs. The prediction of stress distribution can provide the basic guiding theory for the design and implementation of these techniques. In this paper, a fully-coupled three-dimensional production model based on the finite element method (FEM) and fracture continuum method (FCM) for naturally fractured reservoirs is presented to study the effects of fluid consumption on the reservoir stress. Furthermore, the effects of natural fractures on the stress re-distribution and stress re-orientation are also studied. The model also considers the influence of natural fractures on the permeability, and the effect of the effective stress on natural fracture openings, pore-elastic deformation, and fluid consumption. An analytical solution model and Eclipse were used for the comparison, which verifies the accuracy of the model results. Based on two cases of one cluster of fractures and three clusters of non-planar fractures, the research results revealed that natural fractures have a significant influence on the surrounding drainage, stress distribution, and stress re-orientation during the development. Under the influence of natural fractures, the production of the fluid along the direction of natural fractures is significantly easier, and it is highly probably that the insufficient consumption area is perpendicular to the direction of natural fractures. Compared with the conventional model, the stress distribution in the proposed model is deflected to a certain extent under the flow mode dominated by natural fractures, which is significantly prominent in the non-planar fracture model. Due to the effect of natural cracks, the absolute values of the stress, displacement, and stress difference in this model are relatively larger than those in the conventional model. Moreover, the re-orientation angles of the maximum principal stress are significantly different. After considering the natural cracks, there was an increase in the change in re-orientation and the re-orientation range. The research findings reported in this paper can be used to predict the initiation, extension, and steering process of temporary plugging fracturing fractures and refracturing fractures in fractured reservoirs.