We develop a mathematical model to simulate the solidification process of a non-Newtonian power-law fluid flowing through a circular cross-section microchannel. The initial system consists of three partial differential equations, describing the fluid flow and temperature in the liquid and solid, which are solved over a domain specified by the Stefan condition. This is reduced to solving a partially coupled system consisting of a single partial differential equation and the Stefan condition. Results show qualitative differences, depending on the power law index and imposed flow conditions, between Newtonian and non-Newtonian solidification. The model behaviour is illustrated using power law models for blood and polyethylene oxide.