Natural selection and domestication have shaped modern sheep populations into a vast range of phenotypically diverse breeds. Among these breeds, dairy sheep have a smaller population than meat sheep and wool sheep, and less research is performed on them, but the lactation mechanism in dairy sheep is critically important for improving animal-production methods. In this study, whole-genome sequences were generated from 10 sheep breeds, including 57 high-milk-yield sheep and 44 low-milk-yield sheep, to investigate the genetic signatures of milk production in dairy sheep, and 59,864,820 valid SNPs (Single Nucleotide Polymorphisms) were kept after quality control to perform population-genetic-structure analyses, gene-detection analyses, and gene-function-validation analyses. For the population-genetic-structure analyses, we carried out PCA (Principal Component Analysis), as well as neighbor-joining tree and structure analyses to classify different sheep populations. The sheep used in our study were well distributed in ten groups, with the high-milk-yield-group populations close to each other and the low-milk-yield-group populations showing similar classifications. To perform an exact signal-selection analysis, we used three different methods to find SNPs to perform gene-annotation analyses within the 995 common regions derived from the fixation index (FST), nucleotide diversity (Ɵπ), and heterozygosity rate (ZHp) results. In total, we found 553 genes that were located in these regions. These genes mainly participate in the protein-binding pathway and the nucleoplasm-interaction pathway, as revealed by the GO- and KEGG-function-enrichment analyses. After the gene selection and function analyses, we found that FCGR3A, CTSK, CTSS, ARNT, GHR, SLC29A4, ROR1, and TNRC18 were potentially related to sheep-milk-production traits. We chose the strongly selected genes, FCGR3A, CTSK, CTSS, and ARNT during the signal-selection analysis to perform a RT-qPCR (Reale time Quantitative Polymerase Chain Reaction) experiment to validate their expression-level relationship with milk production, and the results showed that FCGR3A has a significant negative relationship with sheep-milk production, while other three genes did not show any positive or negative relations. In this study, it was discovered and proven that the candidate gene FCGR3A potentially contributes to the milk production of dairy sheep and a basis was laid for the further study of the genetic mechanism underlying the strong milk-production traits of sheep.