In critical applications, including search-and-rescue in degraded environments, blockages can be prevalent and prevent the effective deployment of certain sensing modalities, particularly vision, due to occlusion and the constrained range of view of onboard camera sensors. To enable robots to tackle these challenges, we propose a new approach, Proprioceptive Obstacle Detection and Estimation while navigating in clutter PROBE, which instead relies only on the robot's proprioception to infer the presence or absence of occluded rectangular obstacles while predicting their dimensions and poses in SE(2). The proposed approach is a Transformer neural network that receives as input a history of applied torques and sensed whole-body movements of the robot and returns a parameterized representation of the obstacles in the environment. The effectiveness of PROBE is evaluated on simulated environments in Isaac Gym and with a real Unitree Go1 quadruped robot.