We report the first multiplexed microfluidic viscometer capable of measuring simultaneously the viscosity as a function of shear rate for multiple samples. The viscometer is based on a flow-comparator technique where the interface location between co-flowing streams of test and reference fluids is a sensitive function of the viscosity mismatch between the two fluids. We initially design a single microfluidic viscometer and study two different modes of comparator operation - the interface displacement (ID) mode and the interface compensation mode (IC). We find that both modes yield viscosity curves for Newtonian and polymeric fluids that are consistent with a conventional rheometer. Based on the results from the single microfluidic viscometer, we present an operating window that serves as a guide to assess accessible viscosities and shear rates. We then design a 4-plex and 8-plex viscometer based on the ID mode and show that it is capable of reliably measuring viscosity curves for Newtonian fluids, polymeric solutions and consumer products. Collectively, our results demonstrate that the multiplexed viscometer is capable of measuring in a parallel format, viscosities of fluids spanning nearly three orders of magnitude (≈10-3-1 Pa s) across a shear rate range of ≈1-1,000 s-1. We believe our multiplexed viscometer is a low cost and high-throughput alternative to conventional rheometers that analyze samples serially using expensive robotic liquid-handling systems. The multiplexed viscometer could be useful for rapidly analyzing a wide selection of complex fluids on-site during product formulation and quality control.