(1) Background: Despite efforts to improve access to health services, between- and within-country access inequalities remain, especially for individuals with complex disabling conditions like spinal cord injury (SCI). Persons with SCI require regular multidisciplinary follow-up care yet experience more access barriers than the general population. This study examines health system characteristics associated with access among persons with SCI across 22 countries. (2) Methods: Study data are from the International Spinal Cord Injury Survey with 12,588 participants with SCI across 22 countries. Cluster analysis was used to identify service access clusters based on reported access restrictions. The association between service access and health system characteristics (health workforce, infrastructure density, health expenditure) was determined by means of classification and regression trees. (3) Results: Unmet needs were reported by 17% of participants: lowest (10%) in Japan, Spain, and Switzerland (cluster 1) and highest (62%) in Morocco (cluster 8). The country of residence was the most important factor in facilitating access. Those reporting access restrictions were more likely to live in Morocco, to be in the lowest income decile, with multiple comorbidities (Secondary Conditions Scale (SCI-SCS) score > 29) and low functioning status (Spinal Cord Independence Measure score < 53). Those less likely to report access restriction tended to reside in all other countries except Brazil, China, Malaysia, Morocco, Poland, South Africa, and South Korea and have fewer comorbidities (SCI-SCS < 23). (4) Conclusions: The country of residence was the most important factor in facilitating health service access. Following the country of residence, higher income and better health were the most important facilitators of service access. Health service availability and affordability were reported as the most frequent health access barriers.