We present radiance field propagation (RFP), a novel approach to segmenting objects in 3D during reconstruction given only unlabeled multi-view images of a scene. RFP is derived from emerging neural radiance field-based techniques, which jointly encodes semantics with appearance and geometry. The core of our method is a novel propagation strategy for individual objects' radiance fields with a bidirectional photometric loss, enabling an unsupervised partitioning of a scene into salient or meaningful regions corresponding to different object instances. To better handle complex scenes with multiple objects and occlusions, we further propose an iterative expectation-maximization algorithm to refine object masks. To the best of our knowledge, RFP is the first unsupervised approach for tackling 3D scene object segmentation for neural radiance field (NeRF) without any supervision, annotations, or other cues such as 3D bounding boxes and prior knowledge of object class. Experiments demonstrate that RFP achieves feasible segmentation results that are more accurate than previous unsupervised image/scene segmentation approaches, and are comparable to existing supervised NeRF-based methods. The segmented object representations enable individual 3D object editing operations. Codes and datasets will be made publicly available.