It is generally accepted that during the domestication of food plants, selection was focused on their productivity, the ease of their technological processing into food, and resistance to pathogens and environmental stressors. Besides, the palatability of plant foods and their health benefits could also be subjected to selection by humans in the past. Nonetheless, it is unclear whether in antiquity, aside from positive selection for beneficial properties of plants, humans simultaneously selected against such detrimental properties as allergenicity. This topic is becoming increasingly relevant as the allergization of the population grows, being a major challenge for modern medicine. That is why intensive research by breeders is already underway for creating hypoallergenic forms of food plants. Accordingly, in this paper, albumin, globulin, and β-amylase of common wheat Triticum aestivum L. (1753) are analyzed, which have been identified earlier as targets for attacks by human class E immunoglobulins. At the genomic level, we wanted to find signs of past negative selection against the allergenicity of these three proteins (albumin, globulin, and β-amylase) during the domestication of ancestral forms of modern food plants. We focused the search on the TATA-binding protein (TBP)-binding site because it is located within a narrow region (between positions -70 and -20 relative to the corresponding transcription start sites), is the most conserved, necessary for primary transcription initiation, and is the best-studied regulatory genomic signal in eukaryotes. Our previous studies presented our publicly available Web service Plant_SNP_TATA_Z-tester, which makes it possible to estimate the equilibrium dissociation constant (KD) of TBP complexes with plant proximal promoters (as output data) using 90 bp of their DNA sequences (as input data). In this work, by means of this bioinformatics tool, 363 gene promoter DNA sequences representing 43 plant species were analyzed. It was found that compared with non-food plants, food plants are characterized by significantly weaker affinity of TBP for proximal promoters of their genes homologous to the genes of common-wheat globulin, albumin, and β-amylase (food allergens) (p < 0.01, Fisher's Z-test). This evidence suggests that in the past humans carried out selective breeding to reduce the expression of food plant genes encoding these allergenic proteins.