In the present study, Taylor bubble formation in two-phase gas-non-Newtonian Carreau liquid flowing through a confined co-flow microchannel is investigated. Systematic analyses are carried out to explore the influences of rheological properties, inlet velocities, and surface tension on Taylor bubble length, shape, velocity, and liquid film thickness. Aqueous solutions of carboxymethyl cellulose (CMC) with different mass concentrations are considered as the non-Newtonian liquids to understand the fundamentals of flow behaviour. With increasing solution viscosity and liquid phase inlet velocity, Taylor bubble formation frequency and velocity increased; however, the bubble length was found to decrease. Velocity profiles inside the Taylor bubble and liquid slug were analyzed, and distinct velocity distributions were found for different CMC concentrations. Flow regime maps are developed based on gas and liquid velocities for Carreau liquids in the co-flow microchannel. This study essentially provides useful guidelines in designing a non-Newtonian microfluidic system for precise control and manipulation of Taylor bubbles.