This study explored the effect of SARS-CoV-2 infection and COVID-19 vaccination during pregnancy on neonatal outcomes among women from the general Dutch population. VASCO is an ongoing prospective cohort study aimed at assessing vaccine effectiveness of COVID-19 vaccination. Pregnancy status was reported at baseline and through regular follow-up questionnaires. As an extension to the main study, all female participants who reported to have been pregnant between enrolment (May–December 2021) and January 2023 were requested to complete an additional questionnaire on neonatal outcomes. Multivariable linear and logistic regression analyses were used to determine the associations between self-reported SARS-CoV-2 infection or COVID-19 vaccination during pregnancy and neonatal outcomes, adjusted for age, educational level, and presence of a medical risk condition. Infection analyses were additionally adjusted for COVID-19 vaccination before and during pregnancy, and vaccination analyses for SARS-CoV-2 infection before and during pregnancy. Of 312 eligible participants, 232 (74%) completed the questionnaire. In total, 196 COVID-19 vaccinations and 115 SARS-CoV-2 infections during pregnancy were reported. Infections were mostly first infections (86; 75%), caused by the Omicron variant (95; 83%), in women who had received ≥1 vaccination prior to infection (101; 88%). SARS-CoV-2 infection during pregnancy was not significantly associated with gestational age (β = 1.7; 95%CI: −1.6–5.0), birth weight (β = 82; −59 to 223), Apgar score <9 (odds ratio (OR): 1.3; 0.6–2.9), postpartum hospital stay (OR: 1.0; 0.6–1.8), or neonatal intensive care unit admission (OR: 0.8; 0.2–3.2). COVID-19 vaccination during pregnancy was not significantly associated with gestational age (β = −0.4; −4.0 to 3.2), birth weight (β = 88; −64 to 240), Apgar score <9 (OR: 0.9; 0.4–2.3), postpartum hospital stay (OR: 0.9; 0.5–1.7), or neonatal intensive care unit admission (OR: 1.6; 0.4–8.6). In conclusion, this study did not find an effect of SARS-CoV-2 infection or COVID-19 vaccination during pregnancy on any of the studied neonatal outcomes among a general Dutch, largely vaccinated, population. Together with data from other studies, this supports the safety of COVID-19 vaccination during pregnancy.