Speech intelligibility is impacted by dysarthria, a motor speech condition caused by weak, inaccurate, sluggish, or uncoordinated muscular coordination. This paper presents a hybrid deep learning solution using HuBERT (Hidden-Unit BERT) for feature extraction and Deep Neural Network (DNN) for classification. We apply the TORGO dataset with head-mounted microphone recordings to ensure consistent audio quality throughout the dataset. The HuBERT embeddings extracted thereafter are high-level representations of the speech features. These are standardized and introduced into an MLP (multi-layer perceptron) for binary classification, i.e., with or without dysarthria. We have applied a 5-fold cross-validation approach to evaluate model performance, which will provide average scores for F1, recall, and AUC about evaluation. We also perform zero-shot classification by comparing HuBERT features to semantic embeddings using cosine similarity. Feature-level fusion with transformer-based architectures proves beneficial in classifying disordered speech. Hence, it may apply to automated clinical screening and assistive speech technologies.