Background: As social robots increasingly integrate into public spaces, comprehending their security implications becomes paramount. This study is conducted amidst the growing use of social robots in public spaces (SRPS), emphasising the necessity for tailored security standards for these unique robotic systems. Methods: In this systematic mapping study (SMS), we meticulously review and analyse existing literature from the Web of Science database, following guidelines by Petersen et al. We employ a structured approach to categorise and synthesise literature on SRPS security aspects, including physical safety, data privacy, cybersecurity, and legal/ethical considerations. Results: Our analysis reveals a significant gap in existing safety standards, originally designed for industrial robots, that need to be revised for SRPS. We propose a thematic framework consolidating essential security guidelines for SRPS, substantiated by evidence from a considerable percentage of the primary studies analysed. Conclusions: The study underscores the urgent need for comprehensive, bespoke security standards and frameworks for SRPS. These standards ensure that SRPS operate securely and ethically, respecting individual rights and public safety, while fostering seamless integration into diverse human-centric environments. This work is poised to enhance public trust and acceptance of these robots, offering significant value to developers, policymakers, and the general public.