Virtual reality (VR) headsets, with embedded micro-electromechanical systems, have the potential to assess the mechanical heart’s functionality and respiratory activity in a non-intrusive way and without additional sensors by utilizing the ballistocardiographic principle. To test the feasibility of this approach for opportunistic physiological monitoring, thirty healthy volunteers were studied at rest in different body postures (sitting (SIT), standing (STAND) and supine (SUP)) while accelerometric and gyroscope data were recorded for 30 s using a VR headset (Oculus Go, Oculus, Microsoft, USA) simultaneously with a 1-lead electrocardiogram (ECG) signal for mean heart rate (HR) estimation. In addition, longer VR acquisitions (50 s) were performed under controlled breathing in the same three postures to estimate the respiratory rate (RESP). Three frequency-based methods were evaluated to extract from the power spectral density the corresponding frequency. By the obtained results, the gyroscope outperformed the accelerometer in terms of accuracy with the gold standard. As regards HR estimation, the best results were obtained in SIT, with Rs2 (95% confidence interval) = 0.91 (0.81−0.96) and bias (95% Limits of Agreement) −1.6 (5.4) bpm, followed by STAND, with Rs2 = 0.81 (0.64−0.91) and −1.7 (11.6) bpm, and SUP, with Rs2 = 0.44 (0.15−0.68) and 0.2 (19.4) bpm. For RESP rate estimation, SUP showed the best feasibility (98%) to obtain a reliable value from each gyroscope axis, leading to the identification of the transversal direction as the one containing the largest breathing information. These results provided evidence of the feasibility of the proposed approach with a degree of performance and feasibility dependent on the posture of the subject, under the conditions of keeping the head still, setting the grounds for future studies in real-world applications of HR and RESP rate measurement through VR headsets.