Generative Artificial Intelligence (GenAI) tools have gained popularity in Higher Education Institutions (HEIs), and tools such as ChatGPT have been reported to impact students’ cognitive thinking skills. This study addresses a gap in the literature regarding the effect of GenAI on the cognitive thinking skills of students and scholars in HEIs. A Systematic Literature Review (SLR) was conducted that yielded relevant research articles, on which a thematic analysis was performed. Cognitive thinking skills identified in the articles include critical thinking, creative thinking, reflective thinking, computational thinking and problem-solving. The study summarised teaching interventions reported in the various studies, which aimed to engage with and enhance cognitive thinking skills. The findings revealed positive and negative impacts of GenAI on cognitive thinking skills. The findings indicated that GenAI such as ChatGPT can help improve, boost, and develop cognitive thinking skills and enhance learning and the overall higher education experience under well-planned guidance. The study subsequently provides guidelines on how students and scholars can use GenAI to improve cognitive thinking skills in HEIs. HEIs are encouraged to create special programs to teach students how to correctly use GenAI tools like ChatGPT. It is worth noting that students need to use their knowledge, thinking skills, and good judgment to use GenAI properly.