This systematic literature review analyzes how Generative AI (GenAI), specifically Large Language Models (LLMs), impacts Software Product Management (SPM). Based on recent studies, our analysis reveals that current research is in a nascent, experimental phase, focusing on task-level applications like requirements engineering and user persona generation, which show potential for efficiency gains. However, the field suffers from critical limitations, including a lack of methodological standardization, an over-reliance on a narrow range of LLMs like ChatGPT, and a focus on superficial efficiency metrics over measures of product success. We conclude that while LLMs show promise for discrete PM tasks, their true transformative potential lies in integrated, workflow-centric systems. This paper provides a baseline of the current research and calls for a more rigorous, impact-focused agenda for future studies.