The objective of this study was to identify the SNPs and candidate genes related to body weight and seven body conformation traits at the age of 8 months in the Russian aboriginal Karachai goats (n = 269) by conducting genome-wide association studies (GWAS), using genotypes generated by Goat SNP BeadChip (Illumina Inc., San Diego, CA, USA). We identified 241 SNPs, which were significantly associated with the studied traits, including 47 genome-wide SNPs (p < 10−5) and 194 suggestive SNPs (p < 10−4), distributed among all goat autosomes except for autosome 23. Fifty-six SNPs were common for two and more traits (1 SNP for six traits, 2 SNPs for five traits, 12 SNPs for four traits, 20 SNPs for three traits, and 21 SNPs for two traits), while 185 SNPs were associated with single traits. Structural annotation within a window of 0.4 Mb (±0.2 Mb from causal SNPs) revealed 238 candidate genes. The largest number of candidate genes was identified at Chr13 (33 candidate genes for the five traits). The genes identified in our study were previously reported to be associated with growth-related traits in different livestock species. The most significant genes for body weight were CRADD, HMGA2, MSRB3, MAX, HACL1 and RAB15, which regulate growth processes, body sizes, fat deposition, and average daily gains. Among them, the HMGA2 gene is a well-known candidate for prenatal and early postnatal development, and the MSRB3 gene is proposed as a candidate gene affecting the growth performance. APOB, PTPRK, BCAR1, AOAH and ASAH1 genes associated with withers height, rump height and body length, are involved in various metabolic processes, including fatty acid metabolism and lipopolysaccharide catabolism. In addition, WDR70, ZBTB24, ADIPOQ, and SORCS3 genes were linked to chest width. KCNG4 was associated with rump height, body length and chest perimeter. The identified candidate genes can be proposed as molecular markers for growth trait selection for genetic improvement in Karachai goats.