The Cox and Merz rules are empirical correlations between the apparent viscosity of polymers with the effect of shear rate and the complex dynamic viscosity with the effect of frequency. In this study, the rheological properties of mayonnaise-type emulsions enriched with Averrhoa carambola extracts were investigated using small-amplitude oscillatory shear (SAOS) and steady shear flow. The results showed that the shear-thinning behavior of the samples was non-Newtonian with yield stress and had time-dependent characteristics, as evidenced by curves from non-oscillatory measurements. It was observed that the experimental data on the complex and apparent viscosity of the samples obeyed the Cox–Merz rule.