Climate change impacts on health outcomes are increasingly recognized, yet the effects of Extreme Precipitation Events (EPEs) on geographical access to and timely use of health facilities for childbirth remain underexplored. We assess how EPEs influence facility-based births in 21 sub-Saharan African countries by combining Demographic and Health Survey data (2015-2021) with gridded daily precipitation data at 5 × 5 km resolution. Using a linear probability model with a three-day exposure window preceding each date of birth, we analyze 256,101 live births from 12,948 locations and define EPEs as daily rainfall exceeding the 85th percentile of the local historical distribution. We find that each additional day of EPE exposure within the three-day window reduces facility-based births by -10.8 per 1000 live births (95% CI -18.3 to -3.2), representing a 1.9% decrease from baseline. This reduction remains consistent across varying EPE definitions (50th-95th percentile) and becomes less pronounced with longer exposure windows, indicating that events closer to the birth date have greater impact. Sustained moderate to heavy rainfall over multiple days also lowers facility use, indicating that barriers can arise both suddenly and cumulatively. We estimate approximately 29,084 additional non-facility births (95% CI 8660 to 49,508) are attributable to EPEs in 2015. Our findings provide evidence that EPE exposure increases non-facility births that may lack the safety net of skilled attendance and emergency obstetric care.