Accurate detection of drought stress in plants is essential for water use efficiency and agricultural output. Hyperspectral imaging (HSI) provides a non-invasive method in plant phenotyping, allowing the long-term monitoring of plant health due to sensitivity to subtle changes in leaf constituents. The broad spectral range of HSI enables the development of different vegetation indices (VIs) to analyze plant trait responses to multiple stresses, such as the combination of nutrient and drought stresses. However, known VIs may underperform when subjected to multiple stresses. This study presents new VIs in tandem with machine learning models to identify drought stress in wheat plants under varying nitrogen (N) levels. A pot wheat experiment was set up in the glasshouse with four treatments: well-watered high-N (WWHN), well-watered low-N (WWLN), drought-stress high-N (DSHN) and drought-stress low-N (DSLN). In addition to ensuring that plants were watered according to the experiment design, photosynthetic rate (Pn) and stomatal conductance (gs) (which are used to assess plant drought stress) were taken regularly, serving as the ground truth data for this study. The proposed VIs, together with known VIs, were used to train three classification models: support vector machines (SVM), random forest (RF), and deep neural networks (DNN) to classify plants based on their drought status. The proposed VIs achieved more than 0.94 accuracy across all models, and their performance further increased when combined with known VIs. The combined VIs were used to train three regression models to predict the stomatal conductance and photosynthetic rates of plants. The random forest regression model performed best, suggesting that it could be used as a stand-alone tool to forecast gs and Pn and track drought stress in wheat. This study shows that combining hyperspectral data with machine learning can effectively monitor and predict drought stress in crops, especially in varying nitrogen conditions.