Abstract Background In many parts of sub-Saharan Africa, access to abortion is legally restricted, which partly contributes to high incidence of unsafe abortion. This may result in unsafe abortion-related complications that demand long hospital stays, treatment and attendance by skilled health providers. There is however, limited knowledge on the capacity of public health facilities to deliver post-abortion care (PAC), and the spread of PAC services in these settings. We describe and discuss the preparedness and capacity of public health facilities to deliver complete and quality PAC services in Burkina Faso, Kenya and Nigeria. Methods A cross-sectional survey of primary, secondary and tertiary-level public health facilities was conducted between November 2018 and February 2019 in the three countries. Data on signal functions (including information on essential equipment and supplies, staffing and training among others) for measuring the ability of health facilities to provide post-abortion services were collected and analyzed. Results Across the three countries, fewer primary health facilities (ranging from 6.3–12.1% in Kenya and Burkina Faso) had the capacity to deliver on all components of basic PAC services. Approximately one-third (26–43%) of referral facilities across Burkina Faso, Kenya and Nigeria could provide comprehensive PAC services. Lack of trained staff, absence of necessary equipment and lack of PAC commodities and supplies were a main reason for inability to deliver specific PAC services (such as surgical procedures for abortion complications, blood transfusion and post-PAC contraceptive counselling). Further, the lack of capacity to refer acute PAC cases to higher-level facilities was identified as a key weakness in provision of post-abortion care services. Conclusions Our findings reveal considerable gaps and weaknesses in the delivery of basic and comprehensive PAC within the three countries, linked to both the legal and policy contexts for abortion as well as broad health system challenges in the countries. There is a need for increased investments by governments to strengthen the capacity of primary, secondary and tertiary public health facilities to deliver quality PAC services, in order to increase access to PAC and avert preventable maternal mortalities.