Early detection of drought stress in greenhouse tomato (Solanum lycopersicum) is an important issue. Real-time and nondestructive assessment of plant water status is possible by spectroscopy. However, spectral data often suffer from the problems of collinearity, class imbalance, and class overlap, which require some effective strategies to overcome. This study used a spectroscopic dataset on the tomato (cv. ‘Rosada’) vegetative stage and calculated ten spectral reflectance indices (SRIs) to develop an early drought detection model for greenhouse tomatoes. In addition, this study applied the random forest (RF) algorithm and two resampling techniques to explore efficient methods for analyzing multiple SRI data. It was found that the use of the RF algorithm to build a prediction model could overcome collinearity. Moreover, the synthetic minority oversampling technique could improve the model performance when the data were imbalanced. For class overlap in high-dimensional data, this study suggested that two to three important predictors can be screened out, and it then used a scatter plot to decide whether the class overlap should be addressed. Finally, this study proposed an RF model for detecting early drought stress based on three SRIs, namely, RNDVI, SPRI, and SR2, which only needs six spectral wavebands (i.e., 510, 560, 680, 705, 750, and 900 nm) to achieve more than 85% accuracy. This model can be a useful and cost-effective tool for precise irrigation in greenhouse tomato production, and its sensor prototype can be developed and tested in different situations in the future.