Background Health-care resource constraints in low-income and middle-income countries necessitate the identification of cost-effective public health interventions to address COVID-19. We aimed to develop a dynamic COVID-19 microsimulation model to assess clinical and economic outcomes and cost-effectiveness of epidemic control strategies in KwaZulu-Natal province, South Africa. Methods We compared different combinations of five public health interventions: health-care testing alone, where diagnostic testing is done only for individuals presenting to health-care centres; contact tracing in households of cases; isolation centres, for cases not requiring hospital admission; mass symptom screening and molecular testing for symptomatic individuals by community health-care workers; and quarantine centres, for household contacts who test negative. We calibrated infection transmission rates to match effective reproduction number ( R e ) estimates reported in South Africa. We assessed two main epidemic scenarios for a period of 360 days, with an R e of 1·5 and 1·2. Strategies with incremental cost-effectiveness ratio (ICER) of less than US$3250 per year of life saved were considered cost-effective. We also did sensitivity analyses by varying key parameters ( R e values, molecular testing sensitivity, and efficacies and costs of interventions) to determine the effect on clinical and cost projections. Findings When R e was 1·5, health-care testing alone resulted in the highest number of COVID-19 deaths during the 360-day period. Compared with health-care testing alone, a combination of health-care testing, contact tracing, use of isolation centres, mass symptom screening, and use of quarantine centres reduced mortality by 94%, increased health-care costs by 33%, and was cost-effective (ICER $340 per year of life saved). In settings where quarantine centres were not feasible, a combination of health-care testing, contact tracing, use of isolation centres, and mass symptom screening was cost-effective compared with health-care testing alone (ICER $590 per year of life saved). When R e was 1·2, health-care testing, contact tracing, use of isolation centres, and use of quarantine centres was the least costly strategy, and no other strategies were cost-effective. In sensitivity analyses, a combination of health-care testing, contact tracing, use of isolation centres, mass symptom screening, and use of quarantine centres was generally cost-effective, with the exception of scenarios in which R e was 2·6 and when efficacies of isolation centres and quarantine centres for transmission reduction were reduced. Interpretation In South Africa, strategies involving household contact trac...