Multiple sclerosis (MS) is an inflammatory autoimmune disease that causes demyelination of nerve cell axons. This paper is devoted to the study of relapsing-remitting multiple sclerosis (RRMS) biomarkers using an LC-MS/MS-based targeted metabolomics approach and the assessment of changes in the profile of 13 amino acids and 29 acylcarnitines in plasma during the relapse of the disease. A significant increase (p < 0.05) in the concentration of glutamate in plasma in patients with RRMS was detected, while the sum of leucine and isoleucine was reduced. A decrease in the concentration of decenoylcarnitine (C10:1, p < 0.05) was observed among acylcarnitines, and this metabolite was detected as a biomarker for the disease for the first time. Several models based on a single marker or multiple pre-selected markers and multivariate analysis with a dimension reduction technique were compared in their effectiveness for the classification of RRMS and healthy controls. The best results for cross-validation showed models of general linear regression (GLM, AUC = 0.783) and random forest model (RF, AUC = 0.769) based on pre-selected biomarkers. Validation of the models on the test set showed that the RF model based on selected metabolites was the most effective (AUC = 0.72). The results obtained are promising for further development of the system of clinical decision support for the diagnosis of RRMS based on metabolic data.