The COVID-19 pandemic has resulted in substantial mortality worldwide. However, to date, countries in the Middle East and Africa have reported considerably lower mortality rates than in Europe and the Americas. Motivated by reports of an overwhelmed health system, we estimate the likely under-ascertainment of COVID-19 mortality in Damascus, Syria. Using all-cause mortality data, we fit a mathematical model of COVID-19 transmission to reported mortality, estimating that 1.25% of COVID-19 deaths (sensitivity range 1.00% - 3.00%) have been reported as of 2 September 2020. By 2 September, we estimate that 4,380 (95% CI: 3,250 - 5,550) COVID-19 deaths in Damascus may have been missed, with 39.0% (95% CI: 32.5% - 45.0%) of the population in Damascus estimated to have been infected. Accounting for under-ascertainment corroborates reports of exceeded hospital bed capacity and is validated by community-uploaded obituary notifications, which confirm extensive unreported mortality in Damascus.