Leveraging the high temporal resolution and dynamic range, object detection with event cameras can enhance the performance and safety of automotive and robotics applications in real-world scenarios. However, processing sparse event data requires compute-intensive convolutional recurrent units, complicating their integration into resource-constrained edge applications. Here, we propose the Sparse Event-based Efficient Detector (SEED) for efficient event-based object detection on neuromorphic processors. We introduce sparse convolutional recurrent learning, which achieves over 92% activation sparsity in recurrent processing, vastly reducing the cost for spatiotemporal reasoning on sparse event data. We validated our method on Prophesee's 1 Mpx and Gen1 event-based object detection datasets. Notably, SEED sets a new benchmark in computational efficiency for event-based object detection which requires long-term temporal learning. Compared to state-of-the-art methods, SEED significantly reduces synaptic operations while delivering higher or same-level mAP. Our hardware simulations showcase the critical role of SEED's hardware-aware design in achieving energy-efficient and low-latency neuromorphic processing.