Background: Multiple COVID-19 outbreaks have occurred in homeless shelters across the US, highlighting an urgent need to identify the most effective infection control strategy to prevent future outbreaks. Methods: We developed a microsimulation model of SARS-CoV-2 transmission in a homeless shelter and calibrated it to data from cross-sectional polymerase-chain-reaction (PCR) surveys conducted during COVID-19 outbreaks in five shelters in three US cities from March 28 to April 10, 2020. We estimated the probability of averting a COVID-19 outbreak in a representative homeless shelter of 250 residents and 50 staff over 30 days under different infection control strategies, including daily symptom-based screening, twice-weekly PCR testing and universal mask wearing. Results: The proportion of PCR-positive residents and staff at the shelters with observed outbreaks ranged from 2.6% to 51.6%, which translated to basic reproduction number (R0) estimates of 2.9-6.2. The probability of averting an outbreak diminished with higher transmissibility (R0) within the simulated shelter and increasing incidence in the local community. With moderate community incidence (~30 confirmed cases/1,000,000 people/day), the estimated probabilities of averting an outbreak in a low-risk (R0=1.5), moderate-risk (R0=2.9), and high-risk (R0=6.2) shelter were, respectively: 0.33, 0.11 and 0.03 for daily symptom-based screening; 0.52, 0.27, and 0.04 for twice-weekly PCR testing; 0.47, 0.20 and 0.06 for universal masking; and 0.68, 0.40 and 0.08 for these strategies combined. Conclusions: In high-risk homeless shelter environments and locations with high community incidence of COVID-19, even intensive infection control strategies (incorporating daily symptom-screening, frequent PCR testing and universal mask wearing) are unlikely to prevent outbreaks, suggesting a need for non-congregate housing arrangements for people experiencing homelessness. In lower-risk environments, combined interventions should be adopted to reduce outbreak risk.