Deterministic lateral displacement devices have been proved to be an efficient way to perform continuous particle separation in microfluidic applications (Huang et al. Science 304:987-990, 2004). On the basis of their size, particles traveling through an array of obstacles follow different paths and can be separated in outflow. One limitation of such a technique is that each device works for a specific critical size to achieve particle separation, and a new device with different geometrical properties needs to be fabricated, as the dimensions of the particles to be separated change. In this work, we demonstrate the possibility to tune the critical particle size in a deterministic lateral displacement device by using non-Newtonian fluids as suspending liquid. The analysis is carried out by extending the theory developed for a Newtonian constitutive law (Inglis et al. Lab Chip 6:655-658, 2006) to account for fluid shear-thinning. 3-D finite element simulations are performed to compute the dynamics of a spherical particle flowing through the deterministic ratchet. The results show that fluid shear-thinning, by altering the flow field between the obstacles, contributes to decrease the critical particle diameter as compared to the Newtonian case. Numerical simulations demonstrate that tunability of the critical separation size can be achieved by using the flow rate as control parameter. A design formula, relating the separation diameter to the fluid rheology and the relevant geometrical parameters of the device, is derived. Such a formula, originally developed for a power-law model, is proved to work for non-Newtonian liquids with a general viscosity trend.