The SARS-CoV-2 pandemic continues to be a global health concern. The mRNA-1273 (Moderna) vaccine was reported to have an efficacy of 94.1% at preventing symptomatic COVID-19 due to infection with 'wild-type' variants in a randomized clinical trial. Here, we assess the real-world effectiveness of this vaccine against SARS-CoV-2 variants of concern, specifically B.1.1.7 (Alpha) and B.1.351 (Beta), in Qatar, a population that comprises mainly working-age adults, using a matched test-negative, case-control study design. We show that vaccine effectiveness was negligible for 2 weeks after the first dose, but increased rapidly in the third and fourth weeks immediately before administration of a second dose. Effectiveness against B.1.1.7 infection was 88.1% (95% confidence interval (CI): 83.7-91.5%) ≥14 days after the first dose but before the second dose, and was 100% (95% CI: 91.8-100.0%) ≥14 days after the second dose. Analogous effectiveness against B.1.351 infection was 61.3% after the first dose (95% CI: 56.5-65.5%) and 96.4% after the second dose (95% CI: 91.9-98.7%). Effectiveness against any severe, critical or fatal COVID-19 disease due to any SARS-CoV-2 infection (predominantly B.1.1.7 and B.1.351) was 81.6% (95% CI: 71.0-88.8%) and 95.7% (95% CI: 73.4-99.9%) after the first and second dose, respectively. The mRNA-1273 vaccine is highly effective against B.1.1.7 and B.1.351 infections, whether symptomatic or asymptomatic, and against any COVID-19 hospitalization and death, even after a single dose.