Advanced age correlates with higher morbidity and mortality among patients affected with the novel coronavirus disease 2019 (COVID-19). Because systemic inflammation and neurological symptoms are also common in severe COVID-19 cases, there is concern that COVID-19 may lead to neurodegenerative conditions such as Alzheimer’s disease (AD). In this review, we summarize possible mechanisms by which infection with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causative agent of COVID-19, may cause AD in elderly COVID-19 patients and describe preventive measures to mitigate risk. Potential mechanisms include NLRP3 inflammasome activation and IL-1β release, renin-angiotensin system hyperactivation, innate immune activation, oxidative stress, direct viral infection, and direct cytolytic β-cell damage. Anti-inflammatory therapies, including TNF-α inhibitors and nonsteroidal anti-inflammatory drugs, antioxidants such as the vitamin E family, nutritional intervention, physical activity, blood glucose control, and vaccination are proposed as preventive measures to minimize AD risk in COVID-19 patients. Since several risk factors for AD may converge during severe SARS-CoV-2 infection, neurologists should be alert for potential symptoms of AD and actively implement preventive measures in patients presenting with neuropsychiatric symptoms and in high-risk patients such as the elderly.