The SARS-Cov-2 virus (COVID-19) has had a global social and economic impact. Despite the growing evidence, its effects on access and delivery of maternal and child health services in low-income countries are still unclear. This cross-sectional case study was conducted in Mjini Magharibi, Chake Chake, and Ilala districts in Tanzania to help fill this gap. The study combined qualitative and quantitative data collection methods, providing an account of the evolution of the pandemic and the associated control measures in Tanzania. We drew from 34 in-depth interviews, 60 semi-structured interviews, and 14 focus group discussions with key informants, patients, and health providers, and complemented the findings with a review of pandemic reports and health facility records. We followed the Standards for Reporting Qualitative Research (SRQR) to provide an account of the findings. Our account of the pandemic shows that there was at times an inconsistent policy response in Tanzania, with diverse control measures adopted at various stages of the epidemic. There was a perception that COVID-19 services were prioritized during the epidemic at the expense of regular ones. There were reports of reorganisation of health facilities, reallocation of staff, rescheduled antenatal and postnatal clinics, and reduced time for health education and child monitoring. Scarcity of essential commodities was reported, such as vaccines, equipment, and medical supplies. Such perceptions were in part supported by the routine utilization evidence in the three districts, showing a lower uptake of antenatal, postnatal, family planning, and immunization services, as well as fewer institutional deliveries. Our findings suggest that, although the policy response in Tanzania was erratic, it was rather fear of the pandemic itself and diversion of resources to control COVID-19, that may have contributed most to lower the utilization of mother and child services. For future emergencies, it will be crucial to ensure the policy response does not weaken the population’s demand for services.