The performance and productivity of livestock have consistently improved by natural and artificial selection over the centuries. Both these selections are expected to leave patterns on the genome and lead to changes in allele frequencies, but natural selection has played the major role among indigenous populations. Detecting selective sweeps in livestock may assist in understanding the processes involved in domestication, genome evolution and discovery of genomic regions associated with economically important traits. We investigated population genetic diversity and selection signals in this study using SNP genotype data of 14 indigenous sheep breeds from Middle East and South Asia, including six breeds from Iran, namely Iranian Balochi, Afshari, Moghani, Qezel, Zel, and Lori-Bakhtiari, three breeds from Afghanistan, namely Afghan Balochi, Arabi, and Gadik, three breeds from India, namely Indian Garole, Changthangi, and Deccani, and two breeds from Bangladesh, namely Bangladeshi Garole and Bangladesh East. The SNP genotype data were generated by the Illumina OvineSNP50 Genotyping BeadChip array. To detect genetic diversity and population structure, we used principal component analysis (PCA), admixture, phylogenetic analyses, and Runs of homozygosity. We applied four complementary statistical tests, FST (fixation index), xp-EHH (cross-population extended haplotype homozygosity), Rsb (extended haplotype homozygosity between-populations), and FLK (the extension of the Lewontin and Krakauer) to detect selective sweeps. Our results not only confirm the previous studies but also provide a suite of novel candidate genes involved in different traits in sheep. On average, FST, xp-EHH, Rsb, and FLK detected 128, 207, 222, and 252 genomic regions as candidates for selective sweeps, respectively. Furthermore, nine overlapping candidate genes were detected by these four tests, especially TNIK, DOCK1, USH2A, and TYW1B which associate with resistance to diseases and climate adaptation. Knowledge of candidate genomic regions in sheep populations may facilitate the identification and potential exploitation of the underlying genes in sheep breeding.