Are language models culturally biased? It is important that language models conform to the cultural aspects of the communities they serve. However, we show in this paper that language models suffer from a significant bias towards Western culture when handling and generating text in Arabic, often preferring, and producing Western-fitting content as opposed to the relevant Arab content. We quantify this bias through a likelihood scoring-based metric using naturally occurring contexts that we collect from online social media. Our experiments reveal that both Arabic monolingual and multilingual models exhibit bias towards Western culture in eight different cultural aspects (person names, food, clothing, location, literature, beverage, religion, and sports). Models also tend to exhibit more bias when prompted with Arabic sentences that are more linguistically aligned with English. These findings raise concerns about the cultural relevance of current language models. Our analyses show that providing culture-indicating tokens or culturally-relevant demonstrations to the model can help in debiasing.