Garlic (Allium sativum L.) is an economically important, monocotyledonous plant with a strong taste and odor. Drought stress adversely affects its growth, development, and yield, particularly during the bolting/bulbing stage. Herein we performed RNA-seq to assess transcriptomic changes induced by drought stress in bolting/bulbing hardneck garlic plants (Purple Glazer). We observed that drought stress significantly reduced photosynthesis rate, fresh weight, and leaf water content. Transcriptomic analysis of garlic leaves under normal conditions and drought stress led to the identification of 5215 differentially expressed genes (2748 up-and 2467 downregulated). The upregulated DEGs were primarily involved in “biological process”, “metabolic process”, “oxidation-reduction process”, carbohydrate and lipid metabolism, and “proteolysis”, whereas the downregulated DEGs were mainly involved in “biological process” and metabolism of various molecules. In addition, genes encoding abscisic acid biosynthetic and catabolic enzymes, heat shock proteins, and E3 ubiquitin ligases were significantly altered by drought stress, indicating involvement in drought tolerance. A further comparison with the DEGs related to salinity stress-treated garlic revealed 867 and 305 DEGs with a similar and reverse expression alteration tendency, respectively.