The duration of viral shedding is determined by a balance between de novo infection and removal of infected cells. That is, if infection is completely blocked with antiviral drugs (100% inhibition), the duration of viral shedding is minimal and is determined by the length of virus production. However, some mathematical models predict that if infected individuals are treated with antiviral drugs with efficacy below 100%, viral shedding may last longer than without treatment because further de novo infections are driven by entry of the virus into partially protected, uninfected cells at a slower rate. Using a simple mathematical model, we quantified SARS-CoV-2 infection dynamics in non-human primates and characterized the kinetics of viral shedding. We counterintuitively found that treatments initiated early, such as 0.5 d after virus inoculation, with intermediate to relatively high efficacy (30–70% inhibition of virus replication) yield a prolonged duration of viral shedding (by about 6.0 d) compared with no treatment.