Autonomous driving requires information such as the velocity of other vehicles to prevent potential hazards. This work proposes a real-time deep learning-based framework to estimate vehicle speeds from image captures through an onboard camera. Vehicles are detected and tracked by the proposed deep neural networks and a tracking algorithm, which analyzes the trajectories. Finally, a linear regression model estimates the speed of a vehicle based on its position and size in the camera frame. This proposal has been tested with two sequences of the Prevention dataset with satisfactory results. The system can estimate the speed of multiple vehicles simultaneously. It can be integrated easily with onboard computer systems, thus allowing to development of a low-cost solution for speed estimation in an everyday vehicle. The potential applications include vehicle safety systems, driver assistance, and autonomous driving technologies.