Maize (Zea mays L.) is one of the most economically important cereal crops. Though time-consuming and labour-intensive, manually measuring phenotypic traits in the field has been the common practice for maize breeding programs. This study presents a system for automated characterisation of several important plant architectural traits of maize plants under field conditions. An algorithm was developed to extract 3D plant skeletons from point cloud data acquired by side-viewing Time-of-Flight cameras. Plants were detected as 3D lines by Hough transform of the skeleton nodes. By analysing the graph structure of the skeletons with respect to the 3D lines, the point cloud was partitioned into plant instances with the stems and the leaves separated. Furthermore, plant height, plant orientation, leaf angle, and stem diameter were extracted for each plant. The image-derived estimates of traits were compared to manual measurements at multiple growth stages. Satisfactory accuracies in terms of mean absolute error (MAE) and coefficient of determination (R2) were achieved for plant height (before flowering: MAE 0.15 m, R2 0.96; after flowering: MAE 0.054 m, R2 0.83), leaf angle (MAE 2.8°, R2 0.83), and plant orientation (MAE 13°), except for stem diameter due to the limitations of the depth sensor. The results showed that the system was robust and accurate when the plants were imaged from only one side despite occlusions caused by leaves, and the method was applicable to maize plants from an early growth stage to full maturity.