Nuclear magnetic resonance imaging (NMRI or MRI) flow measurements and fundamental principles of capillary flow are combined to determine the shear viscosity of non-Newtonian fluids. Shear viscosity data are obtained over the shear rates inferred from the velocity profile measured using MRI. A single, 3 minute measurement consisting of a MRI-determined velocity profile (also referred to as a dynamic displacement profile or position-displacement correlation) and the corresponding pressure drop produces multiple shear viscosity-shear rate data points. This technique was applied to obtain shear viscosity-shear rate data for an aqueous carboxymethyl cellulose (CMC) solution. Good agreement is found between these data and those measured by conventional rotational rheometry. The potential applications of this MRI-based technique include on-line and in-line monitoring of the shear viscosity of single and multiphase non-Newtonian fluids that can be either opaque or transparent.