Current diagnosis of concussion relies on self-reported symptoms and medical records rather than objective biomarkers. This work uses a novel measurement setup called BioVRSea to quantify concussion status. The paradigm is based on brain and muscle signals (EEG, EMG), heart rate and center of pressure (CoP) measurements during a postural control task triggered by a moving platform and a virtual reality environment. Measurements were performed on 54 professional athletes who self-reported their history of concussion or non-concussion. Both groups completed a concussion symptom scale (SCAT5) before the measurement. We analyzed biosignals and CoP parameters before and after the platform movements, to compare the net response of individual postural control. The results showed that BioVRSea discriminated between the concussion and non-concussion groups. Particularly, EEG power spectral density in delta and theta bands showed significant changes in the concussion group and right soleus median frequency from the EMG signal differentiated concussed individuals with balance problems from the other groups. Anterior–posterior CoP frequency-based parameters discriminated concussed individuals with balance problems. Finally, we used machine learning to classify concussion and non-concussion, demonstrating that combining SCAT5 and BioVRSea parameters gives an accuracy up to 95.5%. This study is a step towards quantitative assessment of concussion.