Facial palsy causes the face to droop due to sudden weakness in the muscles on one side of the face. Computer-added assistance systems for the automatic recognition of palsy faces present a promising solution to recognizing the paralysis of faces at an early stage. A few research studies have already been performed to handle this research issue using an automatic deep feature extraction by deep learning approach and handcrafted machine learning approach. This empirical research work designed a multi-model facial palsy framework which is a combination of two convolutional models—a multi-task cascaded convolutional network (MTCNN) for face and landmark detection and a hyperparameter tuned and parametric setting convolution neural network model for facial palsy classification. Using the proposed multi-model facial palsy framework, we presented results on a dataset of YouTube videos featuring patients with palsy. The results indicate that the proposed framework can detect facial palsy efficiently. Furthermore, the achieved accuracy, precision, recall, and F1-score values of the proposed framework for facial palsy detection are 97%, 94%, 90%, and 97%, respectively, for the training dataset. For the validation dataset, the accuracy achieved is 95%, precision is 90%, recall is 75.6%, and F-score is 76%. As a result, this framework can easily be used for facial palsy detection.