Azo dyes are widely spread in our day life, being heavily used in cosmetics, healthcare products, textile industries, and as artificial food colorants. This intense industrial activity, which inherently includes their own production, inexorably leads to uncontrolled release of dyes into the environment. As emerging pollutants, their detection, particularly in water systems, is a priority. Herein, a fluorescence-based method was employed for the sensitive and selective detection of anionic and neutral azo dyes. Carbon dots (CDs) synthesized from wet pomace (WP), an abundant semi-solid waste of olive mills, were used as probes. An outstanding capability for detection of azo dyes methyl orange (MO) and methyl red (MR) in aqueous solutions was disclosed, which reached a limit of detection (LOD) of 151 ppb for MO. The selectivity of WP-CDs for the anionic azo dye (MO) was established through competitive experiments with other dyes, either anionic (indigo carmine) or cationic (fuchsin, methylene blue, and rhodamine 6G); perchlorate salts of transition metal cations (Cu(II), Co(II), Fe(II), Fe(III), Hg(II), and Pb(II)); and sodium salts of common anions (NO3−, CO32−, Cl−, and SO42−). Evidence has been collected that supports static quenching as the main transduction event underlying the observed quenching of the probe’s fluorescence, combined with a dynamic resonance energy transfer (RET) mechanism at high MO concentrations.