Fine-tuning based concept erasing has demonstrated promising results in preventing generation of harmful contents from text-to-image diffusion models by removing target concepts while preserving remaining concepts. To maintain the generation capability of diffusion models after concept erasure, it is necessary to remove only the image region containing the target concept when it locally appears in an image, leaving other regions intact. However, prior arts often compromise fidelity of the other image regions in order to erase the localized target concept appearing in a specific area, thereby reducing the overall performance of image generation. To address these limitations, we first introduce a framework called localized concept erasure, which allows for the deletion of only the specific area containing the target concept in the image while preserving the other regions. As a solution for the localized concept erasure, we propose a training-free approach, dubbed Gated Low-rank adaptation for Concept Erasure (GLoCE), that injects a lightweight module into the diffusion model. GLoCE consists of low-rank matrices and a simple gate, determined only by several generation steps for concepts without training. By directly applying GLoCE to image embeddings and designing the gate to activate only for target concepts, GLoCE can selectively remove only the region of the target concepts, even when target and remaining concepts coexist within an image. Extensive experiments demonstrated GLoCE not only improves the image fidelity to text prompts after erasing the localized target concepts, but also outperforms prior arts in efficacy, specificity, and robustness by large margin and can be extended to mass concept erasure.