Background: In Ehlers-Danlos syndrome (EDS), a group of monogenic disorders affecting connective tissues, obstructive sleep apnoea (OSA) is highly prevalent in adults. The prevalence of OSA in children with EDS is unknown. Objectives: This prospective cross-sectional study aimed at determining the prevalence of OSA in paediatric EDS patients. Methods: Children with EDS (n = 24) were recruited from the Children’s Hospital Zurich and matched to healthy controls. Participants completed home respiratory polygraphy and questionnaires (Sleep-Related Breathing Disorder Scale [SRBD], Epworth Sleepiness Scale [ESS], and Child Health Questionnaire [CHQ]). The American Academy of Sleep Medicine criteria were applied for OSA diagnosis (obstructive apnoea-hypopnoea index [oAHI] ≥1/h). Conditional logistic regression was used to compare the prevalence of OSA and to adjust for possible confounding. Results: OSA was found in 42% of paediatric EDS patients and in 13% of matched controls (OR = 4.5, 95% CI = 0.97–20.83, p = 0.054). The median oAHI was higher in EDS patients than in controls (0.77/h, IQR = 0.19–1.76, vs. 0.24/h, IQR = 0.0–0.60, p < 0.001 adjusted for age, sex, and BMI z-score). EDS patients had lower scores in most CHQ scales and higher SRBD and ESS scores than controls (0.26, IQR = 0.1–0.35, vs. 0.07, IQR = 0–0.19, p = 0.004); 7 ± 4 vs. 5 ± 4, p = 0.033, respectively). Conclusion: OSA is a previously underestimated EDS-related complication increasing disease burden.