Together with the wide range of possible benefits for the rehabilitation/training of people with multiple sclerosis (pwMS) and other neurologic conditions, exposure to immersive virtual reality (VR) has often been associated with unpleasant symptoms, such as transient dizziness, headache, nausea, disorientation and impaired postural control (i.e., cybersickness). Since these symptoms can significantly impact the safety and tolerability of the treatment, it appears important to correctly estimate their presence and magnitude. Given the existing data scarcity, this study aims to assess the existence and severity of possible adverse effects associated with exposure to immersive VR in a cohort of pwMS using both objective measurements of postural control effectiveness and subjective evaluations of perceived symptoms. To this aim, postural sway under upright quiet posture (in the presence and absence of visual input) of 56 pwMS with an Expanded Disability Status Scale score (EDSS) in the range of 0–6.5 (mean EDSS 2.3) and 33 unaffected individuals was measured before and after a 10-min immersive VR session and at 10 min follow-up on the basis of center of pressure (COP) trajectories. The severity of cybersickness symptoms associated with VR exposure was also self-rated by the participants using the Italian version of the Simulator Sickness Questionnaire (SSQ). Temporary impairments of postural control in terms of significantly increased sway area were observed after the VR session only in pwMS with mild–moderate disability (i.e., EDSS in the range of 2.5–6.5) in the presence of visual input. No changes were observed in pwMS with low disability (EDSS 0–2) and unaffected individuals. In contrast, when the visual input was removed, there was a decrease in sway area (pwMS with mild–moderate disability) and COP path length relating to the use of VR (pwMS with mild–moderate disability and unaffected individuals), thus suggesting a sort of “balance training effect”. Even in this case, the baseline values were restored at follow-up. All participants, regardless of their status, experienced significant post-VR side effects, especially in terms of blurred vision and nausea. Taken together, the findings of the present study suggest that a short immersive VR session negatively (eyes open) and positively (eyes closed) impacts the postural control of pwMS and causes significant disorientation. However, such effects are of limited duration. While it is reasonable to state that immersive VR is sufficiently safe and tolerable to not be contraindicated in the rehabilitation/training of pwMS, in order to reduce possible negative effects and maximize the efficacy, safety and comfort of the treatment, it appears necessary to develop specific guidelines that consider important factors like individual susceptibility, maximum exposure time according to the specific features of the simulation, posture to adopt and protocols to assess objective and perceived effects on participants.