The use of masks as a means of reducing transmission of COVID-19 outside healthcare settings has proved controversial. Masks are thought to have two modes of effect: they prevent infection with COVID-19 in wearers; and prevent transmission by individuals with subclinical infection. We used a simple next-generation matrix approach to estimate the conditions under which masks would reduce the reproduction number of COVID-19 under a threshold of 1. Our model takes into account the possibility of assortative mixing, where mask users interact preferentially with other mask users. We make 3 key observations: 1. Masks, even with suboptimal efficacy in both prevention of acquisition and transmission of infection, could substantially decrease the reproduction number for COVID-19 if widely used. 2. Widespread masking may be sufficient to suppress epidemics where R has been brought close to 1 via other measures (e.g., distancing). 3. “Assortment” within populations (the tendency for interactions between masked individuals to be more likely than interactions between masked and unmasked individuals) would rapidly erode the impact of masks. As such, mask uptake needs to be fairly universal to have an effect. This simple model suggests that widespread uptake of masking could be determinative in suppressing COVID-19 epidemics in regions with R(t) at or near 1.