Keeping the oxygen concentration at the desired physiological limits is a challenging task in cellular microfluidic devices. A good knowledge of affecting parameters would be helpful to control the oxygen delivery to cells. This study aims to provide a fundamental understanding of oxygenation process within a hydrogel-based microfluidic device considering simultaneous mass transfer, medium flow, and cellular consumption. For this purpose, the role of geometrical and hydrodynamic properties was numerically investigated. The results are in good agreement with both numerical and experimental data in the literature. The obtained results reveal that increasing the microchannel height delays the oxygen depletion in the absence of media flow. We also observed that increasing the medium flow rate increases the oxygen concentration in the device; however, it leads to high maximum shear stress. A novel pulsatile medium flow injection pattern is introduced to reduce detrimental effect of the applied shear stress on the cells.