Social media addiction is a behavioral dependency characterized by excessive and compulsive use of social media platforms, leading to negative impacts on various aspects of an individual's life. Bibliometric analysis is a research method used to quantitatively analyze academic literature, such as articles, books, and conference papers. It involves the application of statistical and mathematical tools to study the patterns and trends in scientific publications. This bibliometric study provides a comprehensive analysis of the literature on social media addiction, revealing patterns and dynamics within the field. Utilizing Web of Science for bibliographic data, the study employs advanced bibliometric tools like Biblioshiny and CiteSpace to map the scientific landscape. Annual scientific production, top contributing authors, key sources, trending topics, and thematic maps were identified using Biblioshiny. Additionally, network visualizations, such as co-citation networks of authors, time zone network visualizations of keyword co-occurrence, and timeline network visualizations of country collaborations, were created using CiteSpace. Our findings present an increasing trend in publications over the years, highlighting a growing recognition of social media addiction's significance. We detail the most relevant authors and sources, pinpointing key contributors and influential journals that shape the discourse. Trend topics analysis uncovers the prevalent themes, with "internet addiction" and "adolescents" at the forefront, reflecting the field's concentration on the younger population. The thematic map categorizes the research into motor themes (driving research areas), basic themes (fundamental and well-established areas), and niche themes (specialized and emerging topics), providing insight into the central and evolving topics. The study also delves into the co-occurrence of all keywords and the co-citation of authors, illustrating the interconnected nature of the research community. A timeline network visualization of country collaborations underscores the global scope of research efforts. Importantly, the study identifies critical research gaps such as underexplored demographics and emerging digital concerns and discusses practical implications, including the need for targeted intervention programs and informed policy-making. Collectively, this study charts the trajectory of social media addiction research and lays a foundation for future explorations to address identified lacunae.