We use a compartmental model to project scenarios for the spread of COVID-19 in the city of Manaus, with different degrees of social distancing and isolation of infectious individuals. In a scenario without any containment measures, our projections point to more than 50,000 (simultaneously) infectious individuals before the end of April 2020. Only in a scenario with strict and extensive social distancing (lockdown), implemented and observed as of March 23rd, 2020, would this number be less than 50,000 in the first half of June. Furthermore, an increase in the number of tests or in the collective awareness among the population regarding the importance of strict distancing measures would have only had a significant impact if implemented before the end of March.