Nozzle drip is a critical issue affecting product quality during the tobacco flavoring process. Traditional detection methods are destructive and lack timeliness. This study established a rapid non-destructive detection model for nozzle drip using a push-broom hyperspectral camera (900–1700 nm) to collect spectral and spatial data of flavored cut tobacco samples. Near-infrared hyperspectral imaging (HSI) data of cut tobacco samples were analyzed through chemometric methods, including Principal Component Analysis (PCA) and Support Vector Machine (SVM), to construct a precise identification model for nozzle drip. Results demonstrated that the model effectively distinguished drip-affected samples from non-drip samples. Furthermore, the model exhibited visualization capabilities for monitoring drip distribution, clearly differentiating drip and non-drip regions. This method provides an efficient and non-destructive quality control solution for the standardized flavoring process of cut tobacco, ensuring consistent product quality.