Nongenetic perturbations, such as environmental change or developmental noise, can induce novel phenotypes. If an induced phenotype appears recurrently and confers a fitness advantage, selection may promote its genetic stabilization. Nongenetic perturbations can thus initiate evolutionary innovation. Genetic variation that is not usually phenotypically visible may play an important role in this process. Populations under stabilizing selection on a phenotype that is robust to mutations can accumulate such variation. After nongenetic perturbations, this variation can produce new phenotypes. We here study the relationship between a phenotype's mutational robustness and a population's potential to generate novel phenotypic variation. To this end, we use a well-studied model of transcriptional regulation circuits that are important in many evolutionary innovations. We find that phenotypic robustness promotes phenotypic variability in response to nongenetic perturbations, but not in response to mutation. Our work suggests that nongenetic perturbations may initiate innovation more frequently in mutationally robust gene expression traits.