Neuropathological research suggests the tau pathology of Alzheimer’s disease may originate in brainstem nuclei, yet it remains unknown whether tau-mediated degeneration of brainstem nuclei influences cognitive impairment in prodromal Alzheimer’s disease. The present study examined cognitive domains impacted in prodromal Alzheimer’s disease and brainstem substructure volume in cognitively normal older adults (n = 814) and those with mild cognitive impairment (n = 542). Subsamples of cognitively normal (n = 112) and mild cognitive impairment (n = 202) also had cerebrospinal fluid Alzheimer’s disease biomarker characterization. Region-of-interest and voxel-level analyses related whole brainstem, midbrain, pons, and locus coeruleus volumes to cognition with multiple linear regression models corrected for age, sex, education, apolipoprotein-ε4 carrier status, and MRI magnet strength. Within mild cognitive impairment participants, smaller midbrain and locus coeruleus volumes were significantly related to poorer performance on tests of attention and executive function, and the relationship between locus coeruleus volume and executive abilities remained significant in the mild cognitive impairment subsample with biomarker-confirmed Alzheimer’s disease. A brainstem-masked voxel-wise regression further demonstrated an association between locus coeruleus volume and executive abilities. Brainstem volumes were not significantly related to memory processes. Study findings implicate midbrain and locus coeruleus volume in attention and executive deficits in mild cognitive impairment. Together with prior neuropathological studies, our data suggest a link between Alzheimer’s disease-related degeneration of brainstem nuclei and cognitive deficits in prodromal Alzheimer’s disease.