Organized physical activity (OPA) is an important contributor to physical, social, and emotional health and well-being; however, young people with disabilities are participating at lower rates than their peers without disabilities. This study aimed to (1) compare facilitators and barriers to OPA for young people with disabilities who currently do and do not participate in OPA and (2) to assess whether groups differed in the type of internal and external assets they reported. Parents of 218 young people (41% with a primary diagnosis of autism spectrum disorder) with a diverse representation of disabilities completed an online survey. Young people were categorized as either participants in OPA (n = 131) or non-participants (n = 87) by parent report. Non-participation was significantly predicted by the barrier “there are no activities my child enjoys” and by a lack of children’s motivation and happiness during OPA. Significant internal assets differentiating participants from non-participants were the ability to understand simple instructions, love of sport, and meeting physical activity guidelines. Significant external assets were parent and sibling participation in OPA, school type, and household income. The findings from this study have important implications for the design of public health interventions that aim to promote OPA in young people with disabilities, highlighting the need to make activities enjoyable, promote participation of siblings and parents, and support low-income families to participate.