The internet has spread to most parts of the world and is now making the leap into space. An interplanetary or solar-system internet will require a governance system that can manage the economic, political and social issues that may arise. To address these issues, internet governance will need multi-stakeholder participation from traditional governments, international organizations and the private sector. This paper looks at the challenges facing the development of a space-based internet architecture and how existing UN space governance treaties and terrestrial internet governance could help mitigate these risks.