Developmental plasticity describes the capacity of individuals with the same genotype to induce permanent change in a phenotype depending on a specific external input. One well-studied example of adaptive developmental plasticity is the induction of facultative diapause in insects. Studies investigating the inheritance of diapause induction have suggested diverse genetic origins. However, only few studies have performed genome-wide scans to identify genes affecting the induction decision. Here we compare two populations of the butterfly Pieris napi that differ in the propensity to enter diapause, and despite showing a low genome-wide divergence, we identify a few genomic regions that show high divergence between populations. We then identified a single genomic region associated with diapause induction by genotyping diapausing and directly developing siblings from backcrosses of these populations. This region is located on the Z chromosome and contained three circadian clock genes, cycle, clock, and period. Additionally, period harbored the largest number of SNPs showing complete fixation between populations. We conclude that the heritable basis of between-population variation in the plasticity that determines diapause induction resides on the Z chromosome, with the period gene being the prime candidate for the genetic basis of adaptive plasticity.