Electrochemical sensors with polymeric films as a sensitive layer are of high interest in current electroanalysis. A voltammetric sensor based on multi-walled carbon nanotubes (MWCNTs) and electropolymerized 4-aminobenzoic acid (4-ABA) has been developed for the simultaneous determination of synthetic food azo dyes (sunset yellow FCF and tartrazine). Based on the voltammetric response of the dyes’ mixture, the optimal conditions of electropolymerization have been found to be 30-fold potential scanning between −0.3 and 1.5 V, at 100 mV s−1 in the 100 µmol L−1 monomer solution in phosphate buffer pH 7.0. The poly (4-ABA)-based electrode shows a 10.5-fold increase in its effective surface area and a 17.2-fold lower electron transfer resistance compared to the glassy carbon electrode (GCE). The sensor gives a sensitive and selective response to sunset yellow FCF and tartrazine, with the peak potential separation of 232 mV in phosphate buffer pH 4.8. The electrooxidation parameters of dyes have been calculated. Simultaneous quantification is possible in the dynamic ranges of 0.010–0.75 and 0.75–5.0 µmol L−1 for both dyes, with detection limits of 2.3 and 3.0 nmol L−1 for sunset yellow FCF and tartrazine, respectively. The sensor has been tested on orange-flavored drinks and validated with chromatography.