Convenient 4D modeling of human-object interactions is essential for numerous applications. However, monocular tracking and rendering of complex interaction scenarios remain challenging. In this paper, we propose Instant-NVR, a neural approach for instant volumetric human-object tracking and rendering using a single RGBD camera. It bridges traditional non-rigid tracking with recent instant radiance field techniques via a multi-thread tracking-rendering mechanism. In the tracking front-end, we adopt a robust human-object capture scheme to provide sufficient motion priors. We further introduce a separated instant neural representation with a novel hybrid deformation module for the interacting scene. We also provide an on-the-fly reconstruction scheme of the dynamic/static radiance fields via efficient motion-prior searching. Moreover, we introduce an online key frame selection scheme and a rendering-aware refinement strategy to significantly improve the appearance details for online novel-view synthesis. Extensive experiments demonstrate the effectiveness and efficiency of our approach for the instant generation of human-object radiance fields on the fly, notably achieving real-time photo-realistic novel view synthesis under complex human-object interactions.