Traffic incidents pose substantial hazards to public safety and wellbeing, and accurately estimating their duration is pivotal for efficient resource allocation, emergency response, and traffic management. However, existing research often faces limitations in terms of limited datasets, and struggles to achieve satisfactory results in both prediction accuracy and interpretability. This paper established a novel prediction model of traffic incident duration by utilizing a tabular network-TabNet model, while also investigating its interpretability. The study incorporates various novel aspects. It encompasses an extensive temporal and spatial scope by incorporating six years of traffic safety big data from Tianjin, China. The TabNet model aligns well with the tabular incident data, and exhibits a robust predictive performance. The model achieves a mean absolute error (MAE) of 17.04 min and root mean squared error (RMSE) of 22.01 min, which outperforms other alternative models. Furthermore, by leveraging the interpretability of TabNet, the paper ranks the key factors that significantly influence incident duration and conducts further analysis. The findings emphasize that road type, casualties, weather conditions (particularly overcast), and the number of motor and non-motor vehicles are the most influential factors. The result provides valuable insights for traffic authorities, thus improving the efficiency and effectiveness of traffic management strategies.