Fluid injection and withdrawal in a porous medium create changes in pore pressure that alter effective stresses within the medium. This leads to pore volume changes, which can be described by the poroelastic theory. These changes in pore volume can influence fluid flow processes, such as capillary diffusion and imbibition, potentially altering multiphase flow characteristics in subsurface reservoirs with a focus on oil recovery in the naturally fractured carbonate reservoirs (NFCRs). In this study, a semi‐analytical model is developed to analyze the impact of stress‐dependent spontaneous imbibition. The model allows us to study the influence of stress‐dependent effects on porosity, absolute permeability, relative permeability, and capillary pressure on the imbibition and oil recovery mechanisms of both intact rock and fracture in NFCRs. In order to capture the geomechanical interactions involved, pure compliance poroelastic definitions and nonlinear joint normal stiffness equations are used to assess the deformation of intact rock and fracture, respectively. The model shows that increasing effective confining stress shifts the imbibition capillary pressure curve upward, resulting in improved absorption of the wetting phase into the smaller pores and enhanced extraction of the non‐wetting phase. Model calculations provide a rationale for how and why irreducible water saturation increases during compression of mixed‐wet carbonates and decreases in the case of initially strong water‐wet carbonates. It is also shown how higher relative permeability of the wetting phase leads to a greater diffusion of the wetting phase and improved oil recovery for the less deformed mixed‐wet rock.