Nowadays, Unmanned Aerial Vehicles (UAVs)are becoming increasingly popular facilitated by their extensive availability. Autonomous navigation methods can act as an enabler for the safe deployment of drones on a wide range of real-world civilian applications. In this work, we introduce a self-supervised CNN-based approach for indoor robot navigation. Our method addresses the problem of real-time obstacle avoidance, by employing a regression CNN that predicts the agent's distance-to-collision in view of the raw visual input of its on-board monocular camera. The proposed CNN is trained on our custom indoor-flight dataset which is collected and annotated with real-distance labels, in a self-supervised manner using external sensors mounted on an UAV. By simultaneously processing the current and previous input frame, the proposed CNN extracts spatio-temporal features that encapsulate both static appearance and motion information to estimate the robot's distance to its closest obstacle towards multiple directions. These predictions are used to modulate the yaw and linear velocity of the UAV, in order to navigate autonomously and avoid collisions. Experimental evaluation demonstrates that the proposed approach learns a navigation policy that achieves high accuracy on real-world indoor flights, outperforming previously proposed methods from the literature.