The giant black tiger shrimp (Penaeus monodon) is native to the Indo-Pacific and is the second most farmed penaeid shrimp species globally. Understanding genetic structure, connectivity, and local adaptation among Indo-Pacific black tiger shrimp populations is important for informing sustainable fisheries management and aquaculture breeding programs. Population genetic and outlier detection analyses were undertaken using 10,593 genome-wide SNPs from 16 geographically disparate Indo-Pacific P. monodon populations. Levels of genetic diversity were highest for Southeast Asian populations and were lowest for Western Indian Ocean (WIO) populations. Both neutral (n = 9,930) and outlier (n = 663) loci datasets revealed a pattern of strong genetic structure of P. monodon corresponding with broad geographical regions and clear genetic breaks among samples within regions. Neutral loci revealed seven genetic clusters and the separation of Fiji and WIO clusters from all other clusters, whereas outlier loci revealed six genetic clusters and high genetic differentiation among populations. The neutral loci dataset estimated five migration events that indicated migration to Southeast Asia from the WIO, with partial connectivity to populations in both oceans. We also identified 26 putatively adaptive SNPs that exhibited significant Pearson correlation (p < 0.05) between minor allele frequency and maximum or minimum sea surface temperature. Matched transcriptome contig annotations suggest putatively adaptive SNPs involvement in cellular and metabolic processes, pigmentation, immune response, and currently unknown functions. This study provides novel genome-level insights that have direct implications for P. monodon aquaculture and fishery management practices.