Event cameras produce asynchronous, high-dynamic-range streams well suited for detecting small, fast-moving drones, yet most event-based detectors convert the sparse event stream into dense tensors, discarding the representational efficiency of neuromorphic sensing. We propose SparseVoxelDet, to our knowledge the first fully sparse object detector for event cameras, in which backbone feature extraction, feature pyramid fusion, and the detection head all operate exclusively on occupied voxel positions through 3D sparse convolutions; no dense feature tensor is instantiated at any stage of the pipeline. On the FRED benchmark (629,832 annotated frames), SparseVoxelDet achieves 83.38% mAP at 50 while processing only 14,900 active voxels per frame (0.23% of the T.H.W grid), compared to 409,600 pixels for the dense YOLOv11 baseline (87.68% mAP at 50). Relaxing the IoU threshold from 0.50 to 0.40 recovers mAP to 89.26%, indicating that the remaining accuracy gap is dominated by box regression precision rather than detection capability. The sparse representation yields 858 times GPU memory compression and 3,670 times storage reduction relative to the equivalent dense 3D voxel tensor, with data-structure size that scales with scene dynamics rather than sensor resolution. Error forensics across 119,459 test frames confirms that 71 percent of failures are localization near-misses rather than missed targets. These results demonstrate that native sparse processing is a viable paradigm for event-camera object detection, exploiting the structural sparsity of neuromorphic sensor data without requiring neuromorphic computing hardware, and providing a framework whose representation cost is governed by scene activity rather than pixel count, a property that becomes increasingly valuable as event cameras scale to higher resolutions.