Simple and rapid determination of Sudan I, a synthetic azo dye banned in the food industry over health concerns, is needed to ensure foodstuff safety and quality. In this study, a voltammetric approach based on Sudan I oxidation at the glassy carbon electrode (GCE) modified with manganese dioxide nanorods (MnO2 NRs) dispersed in hexadecyl pyridinium bromide was developed. The effectiveness of MnO2 NRs as a modifier was confirmed by a 7.9- and 9.2-fold increase in the electroactive surface area and the electron transfer rate, respectively, as compared to GCE. The irreversible electrooxidation of Sudan I was found to be accompanied by proton transfer and controlled by both diffusion and surface processes. Differential pulse voltammetry in phosphate buffer pH 6.5 was used for analytical purposes. The linear response of the electrode to Sudan I was shown in the ranges of 0.050–2.5 and 2.5–25 μM, with a detection limit of 13.5 nM. The developed approach was tested on dried and smoked paprika and Atlantic salmon. The obtained recovery values of 99–101% suggest that there is no matrix effect and that the method can be applied in practice.