The present study investigated the association of genetic predisposition for white matter hyperintensities (WMHs) with incident amnestic mild cognitive impairment (aMCI) or Alzheimer’s disease (AD), as well as whether such an association was influenced by age, sex, and cognitive reserve. Overall, 537 individuals without aMCI or dementia at baseline were included. Among them, 62 individuals developed aMCI/AD at follow up. Genetic propensity to WMH was estimated using a polygenic risk score for WMHs (PRS WMH). The association of PRS WMH with aMCI/AD incidence was examined using COX models. A higher PRS WMH was associated with a 47.2% higher aMCI/AD incidence (p = 0.015) in the fully adjusted model. Subgroup analyses showed significant results in the older age group, in which individuals with a higher genetic predisposition for WMHs had a 3.4-fold higher risk for developing aMCI/AD at follow up (p < 0.001), as well as in the lower cognitive reserve (CR, proxied by education years) group, in which individuals with a higher genetic predisposition for WMHs had an over 2-fold higher risk (p = 0.013). Genetic predisposition for WMHs was associated with aMCI/AD incidence, particularly in the group of participants with a low CR. Thus, CR might be a modifier in the relationship between genetic predisposition for WMHs and incident aMCI/AD.