Event-based 3D tracking enables low-latency and high-speed perception, while existing CNN- and Transformer-based trackers struggle to capture long-range spatiotemporal dependencies in sparse, noisy event streams, especially under real-time and efficiency constraints. To address these challenges, we present E-TraMamba, the first Mamba-based framework for 3D feature tracking on event data. This new framework adopts a linear state-space model for efficient long-range modeling and integrates a lightweight affine-transform predictor to maintain stable tracking under motion blur and occlusion. We also design an effective scheme to fuse multi-scale cues -- local spatiotemporal patches, correlation maps, and positional embeddings -- into a unified representation that enables stable and smooth 3D tracking. We construct a large-scale synthetic dataset, named EvD-PointOdyssey, which is generated with monocular rendering and provides synchronized event streams, depth maps, and accurate 3D trajectories for training and evaluating event-based 3D tracking models. Extensive experiments on event-based benchmarks demonstrate that E-TraMamba achieves state-of-the-art performance, delivering over $2\times$ longer feature lifetimes under strict accuracy thresholds (e.g., 0.1 m), with higher tracked-feature ratios and lower RMSE than all baselines. These results make E-TraMamba a strong candidate for low-latency visual odometry, real-time SLAM, and interactive robotics.