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In this paper, we study the task of embodied interactive learning for object detection. Given a set of environments (and some labeling budget), our goal is to learn an object detector by having an agent select what data to obtain labels for. How should an exploration policy decide which trajectory should be labeled? One possibility is to use a trained object detector's failure cases as an external reward. However, this will require labeling millions of frames required for training RL policies, which is infeasible. Instead, we explore a self-supervised approach for training our exploration policy by introducing a notion of semantic curiosity. Our semantic curiosity policy is based on a simple observation -- the detection outputs should be consistent. Therefore, our semantic curiosity rewards trajectories with inconsistent labeling behavior and encourages the exploration policy to explore such areas. The exploration policy trained via semantic curiosity generalizes to novel scenes and helps train an object detector that outperforms baselines trained with other possible alternatives such as random exploration, prediction-error curiosity, and coverage-maximizing exploration.