(1) Background: AI-based solutions could become crucial for the prediction of pregnancy disorders and complications. This study investigated the evidence for applying artificial intelligence methods in obstetric pregnancy risk assessment and adverse pregnancy outcome prediction. (2) Methods: Authors screened the following databases: Pubmed/MEDLINE, Web of Science, Cochrane Library, EMBASE, and Google Scholar. This study included all the evaluative studies comparing artificial intelligence methods in predicting adverse pregnancy outcomes. The PROSPERO ID number is CRD42020178944, and the study protocol was published before this publication. (3) Results: AI application was found in nine groups: general pregnancy risk assessment, prenatal diagnosis, pregnancy hypertension disorders, fetal growth, stillbirth, gestational diabetes, preterm deliveries, delivery route, and others. According to this systematic review, the best artificial intelligence application for assessing medical conditions is ANN methods. The average accuracy of ANN methods was established to be around 80–90%. (4) Conclusions: The application of AI methods as a digital software can help medical practitioners in their everyday practice during pregnancy risk assessment. Based on published studies, models that used ANN methods could be applied in APO prediction. Nevertheless, further studies could identify new methods with an even better prediction potential.