Generative Artificial Intelligence (GAI) models, such as ChatGPT, may inherit or amplify societal biases due to their training on extensive datasets. With the increasing usage of GAI by students, faculty, and staff in higher education institutions (HEIs), it is urgent to examine the ethical issues and potential biases associated with this technology. This scoping review aims to elucidate how biases related to GAI in HEIs have been researched and discussed in recent academic publications. We categorized the potential biases that GAI might cause in the field of higher education. Our findings reveal that while there is meaningful scholarly discussion around bias and discrimination concerning GAI models in the AI field, most articles addressing higher education approach the issue superficially. Few articles identify specific types of bias in different higher education contexts, and there is a notable lack of empirical research. Most papers in our review focus primarily on educational and research fields related to medicine and engineering, with some addressing English education. However, there is almost no discussion regarding the humanities and social sciences. Additionally, a significant portion of the current discourse is in English and primarily addresses English-speaking contexts. To the best of our knowledge, our study is the first to categorize the potential biases that GAI might cause in the field of higher education. This review highlights the need for more in-depth studies and empirical work to understand the specific biases that GAI might introduce or amplify in educational settings, guiding the development of more ethical AI applications in higher education.