We examined associations between mild or asymptomatic prenatal SARS-CoV-2 infection and preterm live birth in a prospective cohort study. During August 2020–October 2021, pregnant persons were followed with systematic surveillance for RT-PCR or serologically-confirmed SARS-CoV-2 infection until pregnancy end. The association between prenatal SARS-CoV-2 infection and preterm birth was assessed using Cox proportional-hazards regression. Among 954 pregnant persons with a live birth, 185 (19%) had prenatal SARS-CoV-2 infection and 123 (13%) had preterm birth. The adjusted hazard ratio for the association between SARS-CoV-2 infection and preterm birth was 1.28 (95% confidence interval 0.82-1.99, p=0.28), although results did not reach statistical significance.