For object detection, capturing the scale of uncertainty is as important as accurate localization. Without understanding uncertainties, self-driving vehicles cannot plan a safe path. Many studies have focused on improving object detection, but relatively little attention has been paid to uncertainty estimation. We present an uncertainty model to predict the standard deviation of bounding box parameters for a monocular 3D object detection model. The uncertainty model is a small, multi-layer perceptron (MLP) that is trained to predict uncertainty for each detected object. In addition, we observe that occlusion information helps predict uncertainty accurately. A new monocular detection model is designed to classify occlusion levels as well as to detect objects. An input vector to the uncertainty model contains bounding box parameters, class probabilities, and occlusion probabilities. To validate predicted uncertainties, actual uncertainties are estimated at the specific predicted uncertainties. The accuracy of the predicted values is evaluated using these estimated actual values. We find that the mean uncertainty error is reduced by 7.1% using the occlusion information. The uncertainty model directly estimates total uncertainty at the absolute scale, which is critical to self-driving systems. Our approach is validated through the KITTI object detection benchmark.