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Large-scale vision-language models such as CLIP have shown impressive performance on zero-shot image classification and image-to-text retrieval. However, such performance does not realize in tasks that require a finer-grained correspondence between vision and language, such as Visual Question Answering (VQA). As a potential cause of the difficulty of applying these models to VQA and similar tasks, we report an interesting phenomenon of vision-language models, which we call the Concept Association Bias (CAB). We find that models with CAB tend to treat input as a bag of concepts and attempt to fill in the other missing concept crossmodally, leading to an unexpected zero-shot prediction. We demonstrate CAB by showing that CLIP's zero-shot classification performance greatly suffers when there is a strong concept association between an object (e.g. eggplant) and an attribute (e.g. color purple). We also show that the strength of CAB predicts the performance on VQA. We observe that CAB is prevalent in vision-language models trained with contrastive losses, even when autoregressive losses are jointly employed. However, a model that solely relies on autoregressive loss seems to exhibit minimal or no signs of CAB.