Background: The COVID-19 pandemic triggered organisational changes in maternity services and support for women, with potential consequences for perinatal and postpartum mental health. Methods: We conducted a rapid review of PubMed/MEDLINE, CINAHL and Web of Science (2020 to 2025). Quantitative studies in pregnant or postpartum women were eligible if they assessed changes in care/support during COVID-19 and measured mental health using validated instruments. We performed a narrative synthesis. Results: Of 243 records identified, five studies were included (Europe, n = 3; Japan, n = 2). Exposure was measured directly in two studies (an unexpected changes index; a no-visitor policy) and by temporal proxy in the remaining studies. In the unexpected changes study, positive screens were 29.3% for depression (Edinburgh Postnatal Depression Scale ≥ 13) and 33.0% for anxiety (Generalized Anxiety Disorder-7 ≥ 10); each additional postpartum change was associated with higher odds of depression (aOR 1.40; 95% CI 1.30 to 1.55). In a case-control study, a no-visitor policy was associated with lower odds of a positive screen at 1 month postpartum (aOR 0.35; 95% CI 0.18 to 0.68). In a repeated national survey, the prevalence of probable depression increased from 10.3% (2014) to 23.9% (2020). Conclusions: Associations were heterogeneous and depended on context, timing and exposure measurement. Preserving postpartum support and continuity of care should be prioritised in future crises.