Access to point-of-care (POC) diagnostics in resource-limited settings, where laboratory-based diagnostics are limited, depends on efficient supply chain management (SCM). This study evaluated the SCM for SARS-CoV-2 POC diagnostic services in resource-limited settings to determine the effect of SCM on accessibility to SARS-CoV-2 POC tests and to identify barriers and enablers of accessibility to SARS-CoV-2 diagnostic services in Mopani District, Limpopo Province, South Africa. We purposively assessed 47 clinics providing POC diagnostic services between June and September 2022. One participant per clinic completed an audit tool developed by the authors with guidance from the World Health Organization and the Management Sciences for Health guidelines. The audit tool evaluated the following SCM parameters: selection, quantification, storage, procurement, quality assurance, distribution, redistribution, inventory management, and human resource capacity. Percentage rating scores between 90–100% indicated that the facility was compliant with SCM guidelines, while rating scores < 90% indicated non-compliance. The clinic audit scores were summarized and compared across clinics and sub-districts. Clinics had compliance scores ranging from 60.5% to 89.2%. Compliance scores were the highest for procurement, redistribution, and quality assurance (all 100%), followed by storage (mean = 95.2%, 95% CI: 90.7–99.7), quantification (mean = 89.4%, 95% CI: 80.2–98.5), and selection (mean = 87.5%, 95% CI: 87.5%–87.5%). Compliance scores were the lowest for inventory management (mean = 53.2%, 95% CI: 47.9%–58.5%), distribution (mean = 48.6%, 95% CI: 44.6%–52.7%), and human resource capacity (mean = 50.6%, 95% CI: 43.3%–58.0%). A significant correlation was found between compliance score and clinic headcount (r = 0.4, p = 0.008), and compliance score and ideal clinic score (r = 0.4, p = 0.0003). Overall, the 47 clinics audited did not comply with international SCM guidelines. Of the nine SCM parameters evaluated, only procurement, redistribution, and quality assurance did not need improvement. All parameters are key in ensuring full functionality of SCM systems and equitable access to SARS-CoV-2 POC diagnostics in resource limited settings.