Exoskeletons are wearable devices closely coupled to the human, which can interact with the musculoskeletal system, e. g., to augment physical and functional capabilities. A main prerequisite for the development and application of exoskeletons is to investigate the human-exoskeleton interaction, particularly in terms of potential inferences with human motor control. Therefore, the purpose of the present study was to investigate whether a passive unilateral lower limb exoskeleton has an impact on static and dynamic reactive balance control. Eleven healthy subjects (22.9 ± 2.5 years, five females) volunteered for this study and performed three different balance tasks: bipedal standing, single-leg standing, and platform perturbations in single-leg standing. All the balance tasks were conducted with and without a passive unilateral lower limb exoskeleton, while force plates and a motion capture system were used to capture the center of pressure mean sway velocity and the time to stabilization, respectively. Dependent t-tests were separately run for both static balance tests, and a repeated-measure analysis of variance with factors exoskeleton and direction of perturbation was calculated for the dynamic reactive balance task. The exoskeleton did not significantly influence postural sway in bipedal stance. However, in single-leg stance, the mediolateral mean sway velocity of the center of pressure was significantly shorter for the exoskeleton condition. For the dynamic reactive balance task, the participants tended to regain stability less quickly with the exoskeleton, as indicated by a large effect size and longer time to stabilization for all directions of perturbation. In summary, the study showed that the exoskeleton provided some assistive support under static conditions, which however may disappear when sufficient stability is available (bipedal stance). Besides, the exoskeleton tended to impair dynamic reactive balance, potentially by impeding adequate compensatory adjustments. These are important findings with strong implications for the future design and application of exoskeletons, emphasizing the significance of taking into account the mechanisms of human motor control.