The BBQ (Bias Benchmark for Question Answering) dataset enables the evaluation of the social biases that language models (LMs) exhibit in downstream tasks. However, it is challenging to adapt BBQ to languages other than English as social biases are culturally dependent. In this paper, we devise a process to construct a non-English bias benchmark dataset by leveraging the English BBQ dataset in a culturally adaptive way and present the KoBBQ dataset for evaluating biases in Question Answering (QA) tasks in Korean. We identify samples from BBQ into three classes: Simply-Translated (can be used directly after cultural translation), Target-Modified (requires localization in target groups), and Sample-Removed (does not fit Korean culture). We further enhance the cultural relevance to Korean culture by adding four new categories of bias specific to Korean culture and newly creating samples based on Korean literature. KoBBQ consists of 246 templates and 4,740 samples across 12 categories of social bias. Using KoBBQ, we measure the accuracy and bias scores of several state-of-the-art multilingual LMs. We demonstrate the differences in the bias of LMs in Korean and English, clarifying the need for hand-crafted data considering cultural differences.