Blood, a multiphase fluid comprised of plasma, blood cells, and platelets, is known to exhibit a shear-thinning behavior at low shear rates and near-Newtonian behavior at higher shear rates. However, less is known about the impact of its multiphase nature on the transition to turbulence. In this study, we experimentally determined the critical Reynolds number at which the flow began to transition to turbulence downstream of eccentric stenosis for whole porcine blood and a Newtonian blood analog (water-glycerin mixture). Velocity profiles for both fluids were measured under steady-state flow conditions using an ultrasound Doppler probe placed 12 diameters downstream of eccentric stenosis. Velocity was recorded at 21 locations along the diameter at 11 different flow rates. Normalized turbulent kinetic energy was used to determine the critical Reynolds number for each fluid. Blood rheology was measured before and after each experiment. Tests were conducted on five samples of each fluid inside a temperature-controlled in vitro flow system. The viscosity at a shear rate of 1000 s−1 was used to define the Reynolds number for each fluid. The mean critical Reynolds numbers for blood and water-glycerin were 470 ± 27.5 and 395 ± 10, respectively, indicating a ∼19% delay in transition to turbulence for whole blood compared to the Newtonian fluid. This finding is consistent with a previous report for steady flow in a straight pipe, suggesting some aspect of blood rheology may serve to suppress, or at least delay, the onset of turbulence in vivo.