Large and rapidly increasing areas of salt-affected soils are posing major challenges for the agricultural sector. Most fields used for the important food crop Triticum aestivum (wheat) are expected to be salt-affected within 50 years. To counter the associated problems, it is essential to understand the molecular mechanisms involved in salt stress responses and tolerance, thereby enabling their exploitation in the development of salt-tolerant varieties. The myeloblastosis (MYB) family of transcription factors are key regulators of responses to both biotic and abiotic stress, including salt stress. Thus, we used the Chinese spring wheat genome assembled by the International Wheat Genome Sequencing Consortium to identify putative MYB proteins (719 in total). Protein families (PFAM) analysis of the MYB sequences identified 28 combinations of 16 domains in the encoded proteins. The most common consisted of MYB_DNA-binding and MYB-DNA-bind_6 domains, and five highly conserved tryptophans were located in the aligned MYB protein sequence. Interestingly, we found and characterized a novel 5R-MYB group in the wheat genome. In silico studies showed that MYB transcription factors MYB3, MYB4, MYB13 and MYB59 are involved in salt stress responses. qPCR analysis confirmed upregulation of the expression of all these MYBs in both roots and shoots of the wheat variety BARI Gom-25 (except MYB4, which was downregulated in roots) under salt stress. Moreover, we identified nine target genes involved in salt stress that are regulated by the four MYB proteins, most of which have cellular locations and are involved in catalytic and binding activities associated with various cellular and metabolic processes.