This prospective observational study aimed to evaluate whether women with SARS-CoV-2 infection during the first trimester of pregnancy are at higher risk of noninvasive prenatal screening test alterations and/or of congenital fetal anomalies at the second-trimester fetal anatomy scan. Maternal symptoms were secondly investigated. The study was carried out on 12-week pregnant women admitted for noninvasive prenatal testing (16 April and 22 June 2020). The cohort had seromolecular tests for SARS-CoV-2, after which they were divided into a positive case group and a negative control group. Both groups had 20-week ultrasound screening. Seventeen out of the 164 women tested positive for SARS-CoV-2 (10.3%). There were no significant differences in mean nuchal translucency thickness or biochemical markers (pregnancy-associated plasma protein A, alpha-fetoprotein, human chorionic gonadotropin, unconjugated estriol) between cases and controls (p = 0.77, 0.63, 0.30, 0.40, 0.28) or in the fetal incidence of structural anomalies at the second-trimester fetal anatomy scan (p = 0.21). No pneumonia or hospital admission due to COVID-19-related symptoms were observed. Asymptomatic or mildly symptomatic SARS-CoV-2 infection during the first trimester of pregnancy did not predispose affected women to more fetal anomalies than unaffected women. COVID-19 had a favorable maternal course at the beginning of pregnancy in our healthy cohort.