Nowadays, mobile robots are playing an important role in different areas of science, industry, academia and even in everyday life. In this sense, their abilities and behaviours become increasingly complex. In particular, in indoor environments, such as hospitals, schools, banks and museums, where the robot coincides with people and other robots, its movement and navigation must be programmed and adapted to robot–robot and human–robot interactions. However, existing approaches are focused either on multi-robot navigation (robot–robot interaction) or social navigation with human presence (human–robot interaction), neglecting the integration of both approaches. Proxemic interaction is recently being used in this domain of research, to improve Human–Robot Interaction (HRI). In this context, we propose an autonomous navigation approach for mobile robots in indoor environments, based on the principles of proxemic theory, integrated with classical navigation algorithms, such as ORCA, Social Momentum, and A*. With this novel approach, the mobile robot adapts its behaviour, by analysing the proximity of people to each other, with respect to it, and with respect to other robots to decide and plan its respective navigation, while showing acceptable social behaviours in presence of humans. We describe our proposed approach and show how proxemics and the classical navigation algorithms are combined to provide an effective navigation, while respecting social human distances. To show the suitability of our approach, we simulate several situations of coexistence of robots and humans, demonstrating an effective social navigation.