Background To determine whether severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, the cause of COVID-19 disease) exposure in pregnancy, compared to non-exposure, is associated with infection-related obstetric morbidity. Methods We conducted a multicentre prospective study in pregnancy based on a universal antenatal screening program for SARS-CoV-2 infection. Throughout Spain 45 hospitals tested all women at admission on delivery ward using polymerase-chain-reaction (PCR) for COVID-19 since late March 2020. The cohort of positive mothers and the concurrent sample of negative mothers was followed up until 6-weeks post-partum. Multivariable logistic regression analysis, adjusting for known confounding variables, determined the adjusted odds ratio (aOR) with 95% confidence intervals (95% CI) of the association of SARS-CoV-2 infection and obstetric outcomes. Main outcome measures: Preterm delivery (primary), premature rupture of membranes and neonatal intensive care unit admissions. Results Among 1009 screened pregnancies, 246 were SARS-CoV-2 positive. Compared to negative mothers (763 cases), SARS-CoV-2 infection increased the odds of preterm birth (34 vs 51, 13.8% vs 6.7%, aOR 2.12, 95% CI 1.32–3.36, p = 0.002); iatrogenic preterm delivery was more frequent in infected women (4.9% vs 1.3%, p = 0.001), while the occurrence of spontaneous preterm deliveries was statistically similar (6.1% vs 4.7%). An increased risk of premature rupture of membranes at term (39 vs 75, 15.8% vs 9.8%, aOR 1.70, 95% CI 1.11–2.57, p = 0.013) and neonatal intensive care unit admissions (23 vs 18, 9.3% vs 2.4%, aOR 4.62, 95% CI 2.43–8.94, p <  0.001) was also observed in positive mothers. Conclusion This prospective multicentre study demonstrated that pregnant women infected with SARS-CoV-2 have more infection-related obstetric morbidity. This hypothesis merits evaluation of a causal association in further research.