Background: The COVID-19 pandemic has positioned fragile healthcare systems in low-income countries under pressure, leading to critical gaps in service delivery. The pandemic response demands the healthcare system to be resilient and continue provision of healthcare services. This review is aimed at describing the healthcare response challenges during the pandemic in Ethiopia. Methodology: Eligible studies dealing with challenges of the healthcare system in response to the COVID-19 pandemic in Ethiopia were included. The six World Health Organization (WHO) healthcare system building blocks were used to categorize healthcare challenges. PubMed ProQuest, databases were searched, and results were summarized using systematic review synthesis. Results: Financial constraints led to a shortage of mechanical ventilators. Furthermore, the pandemic hindered the capacity to avail full packages of personal protective equipment in health facilities and intensive care capacity. The pandemic also affected the delivery of maternal, child and new-born services, prevention, and treatment of childhood illness, including immunization services. Conclusions: The COVID-19 pandemic posed various challenges to the performance of the healthcare system in Ethiopia. It is recommended that policy makers and stakeholders enhance pandemic preparedness and strengthen response capacity by considering the six WHO healthcare system building blocks.