Amino acid metabolism constitutes a major metabolic pathway in plants, playing an important role in the modulation of plant responses to stress. In this study, we investigated the amino acid metabolism responses of M. sativa (Medicago sativa L.) and M. truncatula (Medicago truncatula L.) plants under salt stress using transcriptomic and proteomic approaches to elucidate their salt stress tolerance mechanisms in relation to the regulation of amino acid homeostasis. Transcriptome and proteome sequencing followed by Kyoto Gene and Genome Encyclopedia enrichment analysis revealed 34 differentially expressed genes and 45 differentially expressed proteins involved in valine, leucine, and isoleucine degradation, tyrosine metabolism, and glutathione metabolism. Significant differences were observed in the expression of glutathione S-transferase (GST) within the glutathione metabolic pathway between M. sativa and M. truncatula. The induction of valine, leucine, and isoleucine metabolism, aldehyde dehydrogenases (ALDHs), and alanine-glyoxylate aminotransferases (AGXTs), involved in intracellular reactive oxygen species scavenging, also significantly differed under salt stress. Significant differences were identified in the expression of tyrosine decarboxylases (TDCs) involved in tyrosine metabolism, which are responsible for tyramine biosynthesis and can enhance plant tolerance to salt stress. This study delved into the effects of amino acid metabolism on the salt tolerance mechanisms of M. sativa and M. truncatula, which is crucial in guiding the future breeding of salt-tolerant alfalfa varieties.