BACKGROUND: Healthcare resource constraints in low and middle-income countries necessitate selection of cost-effective public health interventions to address COVID-19. METHODS: We developed a dynamic COVID-19 microsimulation model to evaluate clinical and economic outcomes and cost-effectiveness of epidemic control strategies in KwaZulu-Natal, South Africa. Interventions assessed were Healthcare Testing (HT), where diagnostic testing is performed only for those presenting to healthcare centres; Contact Tracing (CT) in households of cases; Isolation Centres (IC), for cases not requiring hospitalisation; community health worker-led Mass Symptom Screening and molecular testing for symptomatic individuals (MS); and Quarantine Centres (QC), for household contacts who test negative. Given uncertainties about epidemic dynamics in South Africa, we evaluated two main epidemic scenarios over 360 days, with effective reproduction numbers (Re) of 1.5 and 1.2. We compared HT, HT+CT, HT+CT+IC, HT+CT+IC+MS, HT+CT+IC+QC, and HT+CT+IC+MS+QC, considering strategies with incremental cost-effectiveness ratio (ICER) <US$3,250/year-of-life saved (YLS) cost-effective. In sensitivity analyses, we varied Re, molecular testing sensitivity, and efficacies and costs of interventions. FINDINGS: With Re 1.5, HT resulted in the most COVID-19 deaths over 360 days. Compared with HT, HT+CT+IC+MS+QC reduced mortality by 94%, increased costs by 33%, and was cost-effective (ICER $340/YLS). In settings where quarantine centres cannot be implemented, HT+CT+IC+MS was cost-effective compared with HT (ICER $590/YLS). With Re 1.2, HT+CT+IC+QC was the least costly strategy, and no other strategy was cost-effective. HT+CT+IC+MS+QC was cost-effective in many sensitivity analyses; notable exceptions were when Re was 2.6 and when efficacies of ICs and QCs for transmission reduction were reduced. INTERPRETATION: In South Africa, strategies involving household contact tracing, isolation, mass symptom screening, and quarantining household contacts who test negative would substantially reduce COVID-19 mortality and be cost-effective. The optimal combination of interventions depends on epidemic growth characteristics and practical implementation considerations.