Understanding how failure mechanisms and fluid flow patterns develop in response to fluid injection into a dense granular medium is critical to the design and diagnosis of engineering applications such as hydraulic fracturing and waterflooding in unconsolidated formations. In this work, the process of fluid injection with a non-Newtonian fluid is investigated numerically using the distinct element code PFC2D® coupled with a pore network model. The analysis assumes the fluid rheology to be power law. Effects of the injection rate and the rheological parameters on the fluid flow and grain displacement patterns are examined. The numerical results suggest that the near wellbore behaviors in the injection process are governed by the high shear rate rheology. As the injection rate increases, fluid infiltration becomes limited and localized failure characterized by the growth of fractures or fluid channels occurs. As the injection rate becomes large, the breakdown pressure becomes insensitive to the fluid rheology.