Maternal and child health (MCH) has been a global priority for many decades and is an essential public health service. Ensuring seamless delivery is vital for desirable MCH outcomes. This systematic review outlined the challenges in accessing and continuing MCH services during public health emergencies—pandemics and disasters. A comprehensive search approach was built based on keywords and MeSH terms relevant to ‘MCH services’ and ‘pandemics/disasters’. The online repositories Medline, CINAHL, Psyc INFO, and Epistemonikos were searched for studies. We included twenty studies—seven were on the Ebola outbreak, two on the Zika virus, five related to COVID-19, five on disasters, and one related to conflict situations. The findings indicate the potential impact of emergencies on MCH services. Low utilization and access to services have been described as common challenges. The unavailability of personal safety equipment and fear of infection were primary factors that affected service delivery. The available evidence, though limited, indicates the significant effect of disasters and pandemics on MCH. However, more primary in-depth studies are needed to understand better the overall impact of emergencies, especially the COVID-19 pandemic, on MCH. Our synthesis offers valuable insights to policymakers on ensuring the uninterrupted provision of MCH services during an emergency.