Wheat is a cereal grain that plays an important role in the world’s food industry. The identification of the loci that change the concentration of elements in wheat seeds is an important challenge nowadays especially for genomic selection and breeding of novel varieties. In this study, we performed a multivariate genome-wide association study (GWAS) of the seven traits—concentrations of Zn, Mg, Mn, Ca, Cu, Fe, and K in grain—of the Russian collection of common wheat Triticum aestivum (N = 149 measured in two years in two different fields). We replicated one known locus associated with the concentration of Zn (IAAV1375). We identified four novel loci—BS00022069_51 (associated with concentrations of Ca and K), RFL_Contig6053_3082 (associated with concentrations of Fe and Mn), Kukri_rep_c70864_329 (associated with concentrations of all elements), and IAAV8416 (associated with concentrations of Fe and Mn)—three of them were located near the genes TraesCS6A02G375400, TraesCS7A02G094800, and TraesCS5B02G325400. Our result adds novel information on the loci involved in wheat grain element contents and may be further used in genomic selection.