Tartary buckwheat is a type of coarse cereal that contains a rich supply of flavonoids. When suffering from certain stresses, tartary buckwheat can respond by promoting the biosynthesis of anthocyanins. It is well established that the jasmonate (JA) signaling pathway plays a critical role in plant resistance to disease by stimulating the production of anthocyanins; furthermore, the genes encoding the jasmonate-ZIM domain (JAZ) proteins have been shown to be key players in this process. However, the role of JAZ proteins in tartary buckwheat is poorly understood. In this study, we aimed to isolate FtJAZs from tartary buckwheat and identify FtJAZs that are involved in anthocyanin biosynthesis under cold-stress conditions based on an interaction with the known FtMYBs. We identified three novel FtJAZ genes in tartary buckwheat. According to a phylogenetic analysis, FtJAZ1 was organized into cluster I, while FtJAZ2 and FtJAZ3 were organized into cluster II. Interestingly, a yeast two-hybrid assay showed that FtMYB3 interacted only with FtJAZ2. Furthermore, our qRT-PCR results suggested that FtJAZ2, dihydroflavonol-4-reductase, and anthocyanin synthase had similar expression patterns, which is consistent with the accumulation of anthocyanins. Conversely, the expression of FtMYB3 showed an opposite trend, being negatively correlated with the anthocyanin level. In conclusion, by interacting with FtMYB3, FtJAZ2 plays a role in anthocyanin biosynthesis under cold stress.