Incident detection is fundamental for freeway management to reduce non-recurrent congestions and secondary incidents. Recently, machine learning technologies have made considerable progress in the incident detection field, but many still face challenges in uncertainty quantification due to the aleatoric uncertainty of traffic data and the epistemic uncertainty of model deviations. In this study, a Bayesian deep learning method was proposed for freeway incident detection with uncertainty quantification. A convolutional neural network variant was designed on a Bayesian framework, and mechanisms of Bayes by backpropagation and local reparameterization technics were used to update the weight of the proposed model. The predictive uncertainty of the proposed method was modeled jointly by integrating the aleatoric and epistemic uncertainty. The proposed model was tested on the PORTAL dataset and compared with four benchmark models: standard normal deviate, wavelet neural network, long-short term memory neural network, and convolutional neural network. The results show that the proposed model outperforms the baseline methods in terms of accuracy, detection rate and false alarm rate. Perturbation experiments were used to test the robustness of the model against noise. The results indicated that the aleatoric uncertainty of the model remained almost constant under different noise levels. The proposed method may benefit future studies on uncertainty quantification while using machine learning method in incident management and other fields in intelligent transportation systems.