Large volumes of natural gas and oil are stored in low-permeability fractured reservoirs around the world. Extensive field and lab measurements have revealed presence of natural fracture in different scales and their fractal distributions. The log normal distribution of fractures length and width and their consistency throughout the formation is well documented for different basins in the literature, but the mechanical implication and the potential role of these distributions on fluid flow behavior in the rock is not yet studied. This paper provides poroelastic analysis for a single micro-fracture subject to fluid withdrawal (production) through the fracture. Formation is assumed to be a low permeable poroelastic medium. The main drive behind studying this problem was the fact that core flooding measurements in laboratory studies indicate that permeability of tight formations rock samples is in the order of nanodarcy, however the rate of production from the stimulated and even non-stimulated wells are leading us to average values for shale permeability, which are orders of magnitudes higher than the permeability measured in the lab. In this paper, we are trying to verify the role of natural fractures and their poroelastic properties to explain discrepancy in the measured permeability using different methods. To achieve this goal, we provide analytical solution for fracture volume changes due to fluid withdrawal (production). The roles of differential in-situ stress and formation pressure in determining the crack volume changes were found to be significant. The results could be used to relate the significant reduction in production from some of the shale gas wells to the closure of microfractures or even larger non-propped fractures. In general having the knowledge of mechanical and hydraulic behavior of natural micro-fractures in low permeability reservoirs could be a key to predict the production decline in these formations and provide insight to more sophisticated stimulation techniques in future.