This paper presents a novel approach to metric scale reconstruction of a three-dimensional (3D) scene using a monocular camera. Using a sequence of images from a monocular camera with a fixed focus lens, metric distance to a set of features in the environment is estimated from image blur due to defocus. The blur texture ambiguity which causes scale errors in depth from defocus is corrected in an EKF framework that exploits image velocity measurements. We show in real experiments that our method converges to a metric scale, accurate, sparse depth map and 3D camera poses with images from a monocular camera. Therefore, the proposed approach has the potential to enhance robot navigation algorithms that rely on monocular cameras.