The ability of robots to autonomously navigate through 3D environments depends on their comprehension of spatial concepts, ranging from low-level geometry to high-level semantics, such as objects, places, and buildings. To enable such comprehension, 3D scene graphs have emerged as a robust tool for representing the environment as a layered graph of concepts and their relationships. However, building these representations using monocular vision systems in real-time remains a difficult task that has not been explored in depth.<br />This paper puts forth a real-time spatial perception system Mono-Hydra, combining a monocular camera and an IMU sensor setup, focusing on indoor scenarios. However, the proposed approach is adaptable to outdoor applications, offering flexibility in its potential uses. The system employs a suite of deep learning algorithms to derive depth and semantics. It uses a robocentric visual-inertial odometry (VIO) algorithm based on square-root information, thereby ensuring consistent visual odometry with an IMU and a monocular camera. This system achieves sub-20 cm error in real-time processing at 15 fps, enabling real-time 3D scene graph construction using a laptop GPU (NVIDIA 3080). This enhances decision-making efficiency and effectiveness in simple camera setups, augmenting robotic system agility. We make Mono-Hydra publicly available at: https://github.com/UAV-Centre-ITC/Mono_Hydra.