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Background In 2005, the FDA cautioned that exposure to paroxetine, a selective serotonin reuptake inhibitor (SSRI), during the first trimester of pregnancy may increase the risk of cardiac malformations. Since then, the association between maternal use of SSRIs during pregnancy and congenital malformations in infants has been the subject of much discussion and controversy. The aim of this study is to systematically review the associations between SSRIs use during early pregnancy and the risk of congenital malformations, with particular attention to the potential confounding by indication. Methods The study protocol was registered with PROSPERO (CRD42018088358). Cohort studies on congenital malformations in infants born to mothers with first-trimester exposure to SSRIs were identified via PubMed, Embase, Web of Science, and the Cochrane Library databases through 17 January 2018. Random-effects models were used to calculate summary relative risks (RRs). Results Twenty-nine cohort studies including 9,085,954 births were identified. Overall, use of SSRIs was associated with an increased risk of overall major congenital anomalies (MCAs, RR 1.11, 95% CI 1.03 to 1.19) and congenital heart defects (CHD, RR 1.24, 95% CI 1.11 to 1.37). No significantly increased risk was observed when restricted to women with a psychiatric diagnosis (MCAs, RR 1.04, 95% CI 0.95 to 1.13; CHD, RR 1.06, 95% CI 0.90 to 1.26). Similar significant associations were observed using maternal citalopram exposure (MCAs, RR 1.20, 95% CI 1.09 to 1.31; CHD, RR 1.24, 95% CI 1.02 to 1.51), fluoxetine (MCAs, RR 1.17, 95% CI 1.07 to 1.28; CHD, 1.30, 95% CI 1.12 to 1.53), and paroxetine (MCAs, RR 1.18, 95% CI 1.05 to 1.32; CHD, RR 1.17, 95% CI 0.97 to 1.41) and analyses restricted to using women with a psychiatric diagnosis were not statistically significant. Sertraline was associated with septal defects (RR 2.69, 95% CI 1.76 to 4.10), atrial septal defects (RR 2.07, 95% CI 1.26 to 3.39), and respiratory system defects (RR 2.65, 95% CI 1.32 to 5.32). Conclusions The evidence suggests a generally small risk of congenital malformations and argues against a substantial teratogenic effect of SSRIs. Caution is advisable in making decisions about whether to continue or stop treatment with SSRIs during pregnancy. Electronic supplementary material The online version of this article (10.1186/s12916-018-1193-5) contains supplementary material, which is available to authorized users.