Human activities are inherently complex, and even simple household tasks involve numerous object interactions. To better understand these activities and behaviors, it is crucial to model their dynamic interactions with the environment. The recent availability of affordable head-mounted cameras and egocentric data offers a more accessible and efficient means to understand dynamic human-object interactions in 3D environments. However, most existing methods for human activity modeling either focus on reconstructing 3D models of hand-object or human-scene interactions or on mapping 3D scenes, neglecting dynamic interactions with objects. The few existing solutions often require inputs from multiple sources, including multi-camera setups, depth-sensing cameras, or kinesthetic sensors. To this end, we introduce EgoGaussian, the first method capable of simultaneously reconstructing 3D scenes and dynamically tracking 3D object motion from RGB egocentric input alone. We leverage the uniquely discrete nature of Gaussian Splatting and segment dynamic interactions from the background. Our approach employs a clip-level online learning pipeline that leverages the dynamic nature of human activities, allowing us to reconstruct the temporal evolution of the scene in chronological order and track rigid object motion. Additionally, our method automatically segments object and background Gaussians, providing 3D representations for both static scenes and dynamic objects. EgoGaussian outperforms previous NeRF and Dynamic Gaussian methods in challenging in-the-wild videos and we also qualitatively demonstrate the high quality of the reconstructed models.