Since the launch of ChatGPT, Generative AI (GenAI) has transformed virtually every domain, addressing complex problems in areas previously considered insurmountable. At the same time, the adoption of cloud computing for storing confidential data has been rapidly increasing. This swift shift to the cloud has highlighted the critical need for robust data protection measures. In this paper, we merge these two emerging fields to examine how GenAI influences cloud data security. While research on traditional AI-based solutions for cyber threats has been ongoing, the recent surge in GenAI adoption calls for a focused, systematic study to address specific research questions related to GenAI. We formulate 9 research questions and analyze data from 4 major digital repositories (IEEE, Springer, ACM, Wiley) to provide an extensive overview of how GenAI contributes to mitigating key cloud security threats such as Malware, Denial-of-Service (DoS), and Phishing, among others. We also discuss the potential risks posed by GenAI in cloud security and highlight the operational and ethical challenges that impede its widespread adoption. This systematic study aims to provide valuable insights for fellow researchers and IT professionals, guiding them in effectively leveraging GenAI to enhance cloud data security while being mindful of its limitations and challenges.