Drought stress is one of the main factors limiting the high yield and quality of potatoes. Arabinogalactan proteins (AGPs) are an important class of glycoproteins widely present in the cell walls, plasma membranes, and extracellular matrices of higher plants. Among them, fasciclin-like arabinogalactan proteins (FLAs) are involved in plant development, stress responses, and hormone signal regulation. However, little is known about the FLAs gene in potatoes. Based on transcriptome sequencing data, this study screened a drought stress-related candidate FLA gene (StFLA4) through bioinformatics and expression analysis in potatoes. qRT-PCR analysis showed that StFLA4 was induced by drought stress, and its expression decreased with the extension of stress time. Moreover, the relative expression level of StFLA4 in the drought-resistant variety “Kexin 1” was lower than in the drought-sensitive variety “Atlantic”. The StFLA4 protein was located in the cell membrane and interacted with nineteen proteins, mainly related to response to environmental stimulus, cellular response to abiotic stimulus, and cell maturation. After heterologous overexpression of StFLA4 in tobacco, the transgenic plants showed more withered leaves than the wild-type tobacco under drought stress. During the drought stress period, the expression level of StFLA4 in the transgenic plants significantly decreased, and the activity of SOD and POD was significantly lower than that of WT. However, the MDA content was higher than that of WT. These results indicated that StFLA4 negatively regulates the response to drought stress. In addition, in the germination test of potato “Variety V7” tubers, it was found that the variation tendency of StFLA4 expression was along with the concentration of arabinogalactan proteins, and it may participate in the regulation of potato tuber germination. This study lays the foundation for elucidating the function and expression pattern of StFLA4 response to drought stress and tuber germination in potatoes.