Understanding the fundamental mechanism of fracture-matrix fluid exchange is crucial for the modeling of fractured reservoirs. Traditionally, high-resolution simulations for flow in fractures often neglect the matrix-fracture leakage influence on the fracture hydraulic properties, i.e., assuming impermeable fracture walls. This work introduces a micro-continuum approach to capture the matrix-fracture leakage interaction and its effect on the rock fractures’ hydraulic properties. Because of the multiscale nature of fractured media, full physics Navier-Stokes (NS) representation everywhere in the whole domain is not feasible. We thus employ NS equations to describe the flow in the fracture, and Darcy’s law to model the flow in the surrounding porous rocks. Such hybrid modeling is achieved using the extended Darcy-Brinkman-Stokes (DBS) equation. With this approach, a unified conservation equation for flow in both media is applied by choosing appropriate parameters (e.g., porosity and permeability) for the corresponding domains. We apply an accurate Mixed Finite Element approach to solve the extended DBS equation. Various sensitivity analyses are conducted to explore the leakage effects on the fracture hydraulic properties by varying surrounding matrix permeability, fracture roughness, and Reynolds number (Re). Streamline profiles show the presence of back-flow phenomena, where in-flow and out-flow are possible between the matrix and the fractures. Further, zones of stagnant (eddy) flow are observed around locations with large asperities of sharp corners under high Re conditions. Numerical results show the significant effects of roughness and inertia on flow predictions in fractures for both impermeable and leaky wall cases. Besides, the side-leakage effect can create non-uniform flow behavior within the fracture that may differ significantly from the case with impermeable wall conditions. And this matrix-fracture leakage influence on hydraulic properties of rock fractures matters especially for cases with high matrix permeability, high fracture roughness, and low Re values. In summary, we present a high-resolution micro-continuum approach to explore the flow exchange behavior between the fracture and rock matrix, and further investigate the static and dynamic effects, including variable Reynold numbers, mimicking flow near and away from the wellbore. The approach and results provide significant insights into the flow of fluids through fractures within permeable rocks and can be readily applied in field-scale reservoir simulations.