In this paper, we present a novel approach to integrating virtual reality (VR) into a web-based medical visualization framework. The framework supports visualization of volumetric data, such as 3D scalar fields acquired by a CT, MRI or PET scanners. To improve users' perception, understanding and manipulation of 3D volumes, we adapted the traditional 2D screen representation with support for visualization of data in a VR environment. By providing complete visual immersion, VR can help users to gain better insights and understanding of the visualized data. Our main goal was to allow users to view the medical data in VR and interact with it with hand-held controllers for better immersion and spatial perception. In the paper, we present a novel approach to implementation of VR for medical imaging, which combines WebGL-based hardware accelerated web visualization with VR. This allows users to use the visualization framework with or without a VR headset by switching between "standard" and "VR" modes. Since visualization runs in a web browser, it is portable, easy to use on different devices and therefore accessible to a broad number of users. The visualization system was tested with real medical scans to assess its performance and usability.