Compared with other primates, humans sleep less and have a much higher prevalence of Alzheimer ’s disease (AD) pathology. This article reviews evidence relevant to the hypothesis that natural selection for shorter sleep time in humans has compromised the efficacy of physiological mechanisms that protect against AD during sleep. In particular, the glymphatic system drains interstitial fluid from the brain, removing extra-cellular amyloid beta (eAβ) twice as fast during sleep. In addition, melatonin - a peptide hormone that increases markedly during sleep - is an effective antioxidant that inhibits the polymerization of soluble eAβ into insoluble amyloid fibrils that are associated with AD. Sleep deprivation increases plaque formation and AD, which itself disrupts sleep, potentially creating a positive feedback cycle. These and other physiological benefits of sleep may be compromised by short sleep durations. Our hypothesis highlights possible long-term side effects of medications that reduce sleep, and may lead to potential new strategies for preventing and treating AD.