The genomic organization, phylogenetic relationship, expression patterns, and genetic variations of m6A-related genes were systematically investigated in wild emmer wheat and the function of TdFIP37 regulating salt tolerance was preliminarily determined. m6A modification is one of the most abundant and crucial RNA modifications in eukaryotics, playing the indispensable role in growth and development as well as stress response in plants. However, its significance in wild emmer wheat remains elusive. Here, a genome-wide search of m6A-related genes was conducted in wild emmer wheat to obtain 64 candidates, including 21 writers, 17 erasers, and 26 readers. Phylogenetic and collinearity analysis demonstrated that segmental duplication and polyploidization contributed mainly to the expansion of m6A-related genes in wild emmer. A number of cis-acting elements involving in stress and hormonal regulation were found in the promoter regions of them, such as MBS, LTR, and ABRE. Genetic variation of them was also investigated using resequencing data and obvious genetic bottleneck was occurred on them during wild emmer wheat domestication process. Furthermore, the salt-responsive candidates were investigated through RNA-seq data and qRT-PCR validation using the salt-tolerant and -sensitive genotypes and the co-expression analysis showed that they played the hub role in regulating salt stress response. Finally, the loss-function mutant of Tdfip37 displayed the significantly higher salt-sensitive compared to WT and then RNA-seq analysis demonstrated that FIP37 mediated the MAPK pathway, hormone signal transduction, as well as transcription factor to regulate salt tolerance. This study provided the potential m6A genes for functional analysis, which will contribute to better understand the regulatory roles of m6A modification and also improve the salt tolerance from the perspective of epigenetic approach in emmer wheat and other crops.