Inter-well frac-hit has become an important challenge in the development of unconventional oil and gas resources such as fractured tight sandstone. Due to the presence of hydraulic fracturing fractures, secondary induced fractures, natural fractures, and other seepage media in real formations, the acquisition of stress fields requires the coupling effect of seepage and stress. In this process, there is also stress sensitivity, which leads to unclear dynamic evolution laws of stress fields and increases the difficulty of the staged multi-cluster fracturing of horizontal wells. The use of a multi-stage stress-sensitive horizontal well production stress field prediction model is an effective means of analyzing the influence of natural fracture parameters, main fracture parameters, and multi-stage stress sensitivity coefficients on the stress field. This article considers multi-stage stress sensitivity and, based on fractured sandstone reservoir parameters, establishes a numerical model for the dynamic evolution of the production stress field in horizontal wells with matrix self-supporting fracture-supported fracture–seepage–stress coupling. The influence of various factors on the production stress field is analyzed. The results show that under constant pressure production, for low-permeability reservoirs, multi-stage stress sensitivity has a relatively low impact on reservoir stress, and the amplitude of principal stress change in the entire fracture length direction is only within the range of 0.27%, with no significant change in stress distribution; The parameters of the main fracture have a significant impact on the stress field, with a variation amplitude of within 2.85%. The ability of stress to diffuse from the fracture tip to the surrounding areas is stronger, and the stress concentration area spreads from an elliptical distribution to a semi-circular distribution. The random natural fracture parameters have a significant impact on pore pressure. As the density and angle of the fractures increase, the pore pressure changes within the range of 3.32%, and the diffusion area of pore pressure significantly increases, making it easy to communicate with the reservoir on both sides of the fractures.