The numbers of deaths caused by HIV could increase substantially if the COVID-19 epidemic leads to interruptions in the availability of HIV services. We compare publicly available scenarios for COVID-19 mortality with predicted additional HIV-related mortality based on assumptions about possible interruptions in HIV programs. An interruption in the supply of ART for 40% of those on ART for 3 months could cause a number of deaths on the same order of magnitude as the number that are anticipated to be saved from COVID-19 through social distancing measures. In contrast, if the disruption can be managed such that the supply and usage of ART is maintained, the increase in AIDS deaths would be limited to 1% over five years, although this could still be accompanied by substantial increases in new HIV infections if there are reductions in VMMC, oral PrEP use, and condom availability.