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High-energy electron beam and X-ray processing of foods can be used for the sterilization purposes, and the treatment of seed potatoes can reduce its field damage by pests and diseases. Chromatography–mass-spectrometry methods demonstrated notable changes in the chemical composition of treated foods, but it is not an affordable technique. This paper is aimed at developing more simple methods for revealing the fact of radiation treatment of potato tubers and approximate dose detection. We used a “fingerprinting” strategy that does not involve the determination of the amount of any particular chemical compound; instead, the effect of the potato extracts on the rate of indicator reactions with the participation of carbocyanine dyes is measured: one type of reaction is catalytic oxidation of the dye and the other involves an aggregational process. The dye content was followed by its near-IR fluorescence intensity and visible light absorption. The potatoes not subjected to treatment or irradiated with different doses (10, 100, 1,000 and 10,000 Gray) yielded different signals and eventually different patterns in the score plots of principal component and discriminant analysis. Non-irradiated tubers can be confidently distinguished from those irradiated with a high dose, and the order of the dose received can be estimated with 89–100% accuracy.