Pregnancy and menopause are critical periods in a woman’s life. Due to physiological changes in the neuroendocrine system regulation, susceptibility to respiratory viral infections increases in these periods, while affecting all organs and systems of the human body. The aim of this review was to analyze the literature data on the effect of acute respiratory viral infections on neuroendocrine regulation in women during pregnancy and menopause. We reviewed full-text publications in the public domain from the PubMed, eLibrary.ru, and Google Scholar databases with a coverage period of more than twenty years (2000–2023). Disruptions of the progesterone and estrogen production during infection with the influenza A (H1N1) and influenza B viruses have been shown in experimental studies. Hormonal status changes in pregnant women are detected during infection with the influenza A virus (H3N2) and depend on antiviral antibody titers and the presence of fetoplacental insufficiency. Pregnant women with COVID-19 may experience changes in the brain structure activities, as indicated by a high frequency of those in olfactory sensitivity and psychoemotional disorders. During menopause, infection with the SARS-CoV-2 virus leads to changes in the production of thyroxine, prolactin, estradiol, testosterone, cortisol, 17-hydroxyprogesterone, and dehydroepiandrosterone sulfate.