Event cameras report asynchronously per-pixel brightness changes with microsecond latency, encoding dynamic visual information as a sparse stream of events. However, their extreme temporal resolution floods perception systems with entangled events from ego-motion and independently moving objects (IMOs), which existing solutions fail to efficiently de- couple, relying instead on prohibitive dense 3D reconstructions or limited hand-tuned filters. In this work, we introduce the first framework for Motion-aware Event Suppression, which learns to filter events triggered by IMOs and ego-motion in real time. Our model jointly segments IMOs in the current event stream while predicting their future motion, enabling anticipatory suppression of dynamic events before they occur. Our lightweight architecture achieves 173 Hz inference on consumer-grade GPUs with less than 1 GB of memory usage, outperforming previous state-of-the- art methods on the challenging EVIMO benchmark by 67% in segmentation accuracy while operating at a 53% higher inference rate. Moreover, we demonstrate significant benefits for down- stream applications: our method accelerates Vision Transformer inference by 83% via token pruning and improves event-based visual odometry accuracy, reducing Absolute Trajectory Error (ATE) by 13%.