Patch-based models, e.g., Vision Transformers (ViTs) and Mixers, have shown impressive results on various visual recognition tasks, alternating classic convolutional networks. While the initial patch-based models (ViTs) treated all patches equally, recent studies reveal that incorporating inductive bias like spatiality benefits the representations. However, most prior works solely focused on the location of patches, overlooking the scene structure of images. Thus, we aim to further guide the interaction of patches using the object information. Specifically, we propose OAMixer (object-aware mixing layer), which calibrates the patch mixing layers of patch-based models based on the object labels. Here, we obtain the object labels in unsupervised or weakly-supervised manners, i.e., no additional human-annotating cost is necessary. Using the object labels, OAMixer computes a reweighting mask with a learnable scale parameter that intensifies the interaction of patches containing similar objects and applies the mask to the patch mixing layers. By learning an object-centric representation, we demonstrate that OAMixer improves the classification accuracy and background robustness of various patch-based models, including ViTs, MLP-Mixers, and ConvMixers. Moreover, we show that OAMixer enhances various downstream tasks, including large-scale classification, self-supervised learning, and multi-object recognition, verifying the generic applicability of OAMixer