A numerical model for cavitation in blood is developed based on the Keller-Miksis equation for spherical bubble dynamics with the Carreau model to represent the non-Newtonian behavior of blood. Three different pressure waveforms driving the bubble oscillations are considered: a single-cycle Gaussian waveform causing free growth and collapse, a sinusoidal waveform continuously driving the bubble, and a multi-cycle pulse relevant to contrast-enhanced ultrasound. Parameters in the Carreau model are fit to experimental measurements of blood viscosity. In the Carreau model, the relaxation time constant is 5-6 orders of magnitude larger than the Rayleigh collapse time. As a result, non-Newtonian effects do not significantly modify the bubble dynamics but do give rise to variations in the near-field stresses as non-Newtonian behavior is observed at distances 10-100 initial bubble radii away from the bubble wall. For sinusoidal forcing, a scaling relation is found for the maximum non-Newtonian length, as well as for the shear stress, which is 3 orders of magnitude larger than the maximum bubble radius.