Although edge-tolerant species are known to benefit from habitat fragmentation, less is known about the population genetic impacts fragmentation may exert on edge-tolerant species. We examined the landscape genomic structure of an edge-tolerant forest-dependent bird species, the Striped Tit-Babbler Mixornis gularis, in the heavily urbanized island of Singapore to determine if two centuries of fragmentation have led to signs of isolation and loss of population-genetic diversity in different parts of the island. We obtained a high-quality complete reference genome with 78x coverage. Using almost 4000 SNPs from double-digest RAD-Sequencing across 46 individuals, we found that the population has likely experienced a recent contraction in effective population size and presently exhibits low population genetic diversity. Using empirical and simulation-based landscape genomic analyses, we also found that the subtle population genetic structure observed in the Striped Tit-Babbler population in Singapore is likely driven by isolation by distance resulting from limited dispersal. Our results demonstrate that population genetic impoverishment and subdivision can accumulate at relatively rapid rates in edge-tolerant bird species such as the Striped Tit-Babbler as a result of fragmentation, and that subtle spatial genetic structure can be detected over fine spatial and temporal scales using relatively few multilocus genomic SNPs.