More species than ever before are at risk of extinction due to anthropogenic habitat loss and climate change. But even species that are not threatened have seen reductions in their populations and geographic ranges, likely impacting their genetic diversity. Although preserving genetic diversity is a key conservation target to maintain the adaptability of species, we lack predictive tools and global estimates of genetic diversity loss across ecosystems. By bridging biodiversity and population genetics theories, we introduce the first mathematical framework to understand the loss of naturally occurring DNA mutations within a species--what we call genetic diversity extinction. Analyzing genome-wide variation data of 10,126 geo-tagged individuals from 19 plant and animal species, we show that genome-wide diversity follows a power law with geographic area, which can predict genetic diversity decay in simulated spatial extinctions. Given pre-21st century values of ecosystem transformations, we estimate that over 10% of genetic diversity may be extinct, already surpassing the United Nations targets for genetic preservation. These estimated losses could rapidly increase with advancing climate change and habitat destruction, highlighting the need for new forecasting tools that assist in the rapid implementation of policies to protect genetic resources.