Alzheimer’s disease (AD) affects cognitive modalities that are known to be regulated by adult neurogenesis, such as hippocampal‐ and olfactory‐dependent learning and memory. However, the relationship between AD‐associated pathologies and alterations in adult neurogenesis has remained contentious. In the present study, we performed a detailed investigation of adult neurogenesis in the triple transgenic (3xTg) mouse model of AD, a unique model that generates both amyloid plaques and neurofibrillary tangles, the hallmark pathologies of AD. In both neurogenic niches of the brain, the hippocampal dentate gyrus and forebrain subventricular zone, we found that 3xTg mice had decreased numbers of (i) proliferating cells, (ii) early lineage neural progenitors, and (iii) neuroblasts at middle age (11 months old) and old age (18 months old). These decreases correlated with major reductions in the addition of new neurons to the respective target areas, the dentate granule cell layer and olfactory bulb. Within the subventricular zone niche, cytological alterations were observed that included a selective loss of subependymal cells and the development of large lipid droplets within the ependyma of 3xTg mice, indicative of metabolic changes. Temporally, there was a marked acceleration of age‐related decreases in 3xTg mice, which affected multiple stages of neurogenesis and was clearly apparent prior to the development of amyloid plaques or neurofibrillary tangles. Our findings indicate that AD‐associated mutations suppress neurogenesis early during disease development. This suggests that deficits in adult neurogenesis may mediate premature cognitive decline in AD.