In plants, the synthesis of L-ascorbic acid (Aa), in addition to the main L-galactose pathway, is carried out by three known alternative pathways. One of them, the D-galacturonic acid pathway, is thought to be specific for tissues with excess D-galacturonate, the substrate of D-galacturonate reductase (GalUR), which belongs to the Aldo-Keto Reductase (AKR) superfamily. In this study, the AKR gene family of garlic Allium sativum L. was identified and seven genes, AsGalUR1–7, presumably encoding GalUR enzymes, were determined. The structure and phylogeny of the AsGalUR1–7 genes and the proteins they encode, as well as the AsGalUR1–7 expression pattern in different organs of the garlic plant (in silico and qRT-PCR), were characterized. Based on the obtained data, the genes were conditionally divided into root (AsGalUR1–4) and leaf (AsGalUR5–7) groups depending on the highest expression level in the underground and aboveground parts of the plant, respectively. The AsGalUR expression in leaves and roots was analyzed in response to drought, salt and cold stresses, as well as exogenous phytohormones (abscisic acid, methyl jasmonate), accompanied by the AsA content measurement. It was shown that hormone treatment suppresses the expression of all analyzed genes in both organ types. Cold conditions stimulate the expression of root group genes and suppress that of leaf group genes in roots, and have the opposite effect in leaves. Osmotic stressors (NaCl, PEG) suppress the transcription of all genes in leaves, but do not change (NaCl) or stimulate (PEG) it in roots, which is accompanied by an increase in AsA accumulation in organs of both types. A positive correlation between the expression of the AsGalUR1 and 4 genes and the AsA content is found in leaves under stress conditions. The data obtained can form the basis for further study of the mechanisms regulating AsA synthesis in garlic and other Allium species.