Recent significant progress in Virtual Reality (VR) applications and environments raised several challenges. They proved to have side effects on specific users, thus reducing the usability of the VR technology in some critical domains, such as flight and car simulators. One of the common side effects is cybersickness. Some significant commonly reported symptoms are nausea, oculomotor discomfort, and disorientation. To mitigate these symptoms and consequently improve the usability of VR systems, it is necessary to predict the incidence of cybersickness. This paper proposes a machine learning approach to VR’s cybersickness prediction based on physiological and subjective data. We investigated combinations of topological data analysis with a range of classifier algorithms and assessed classification performance. The highest performance of Topological Data Analysis (TDA) based methods was achieved in combination with SVMs with Gaussian RBF kernel, indicating that Gaussian RBF kernels provide embeddings of physiological time series data into spaces that are rich enough to capture the essential geometric features of this type of data. Comparing several combinations with feature descriptors for physiological time series, the performance of the TDA + SVM combination is in the top group, statistically being on par or outperforming more complex and less interpretable methods. Our results show that heart rate does not seem to correlate with cybersickness.