The evolutionary reasons for sleep remain controversial. The immune theory of sleep suggests that sleep is essential to the immune system, allowing organisms to allocate more energy to their immunity. This hypothesis was tested by exploring the links between excessive daytime sleepiness (EDS) and vulnerability to infectious diseases in a large (n = 9294) cohort of elderly individuals, with information on socio-demographics, daily habits, and medical characteristics. At the two-year and four-year follow-ups, we obtained individual data from the national healthcare insurance about all medications prescribed to the participants between 2001 and 2003 (n = 2865). We found an independent positive association between EDS and the consumption of some anti-pathogen drugs. This relationship was mostly explained by fungal and parasitic infections rather than by viral and bacterial ones. These results, although based on correlations, are consistent with the idea that EDS as a proxy of altered sleep quality/quantity may affect the efficiency of the immune system, and hence vulnerability to infections.