Accurate diagnosis of knee joint injuries from magnetic resonance (MR) images is critical for patient care. Background/Objectives: While deep learning has advanced 3D MR image analysis, its reliance on extensive labeled datasets is a major hurdle for diverse knee pathologies. Few-shot learning (FSL) addresses this by enabling models to classify new conditions from minimal annotated examples, often leveraging knowledge from related tasks. However, creating robust 3D FSL frameworks for varied knee injuries remains challenging. Methods: We introduce MedNet-FS, a 3D FSL framework that effectively classifies knee injuries by utilizing domain-specific pre-trained weights and generalized end-to-end (GE2E) loss for discriminative embeddings. Results: MedNet-FS, with knee-MRI-specific pre-training, significantly outperformed models using generic or other medical pre-trained weights and approached supervised learning performance on internal datasets with limited samples (e.g., achieving an area under the curve (AUC) of 0.76 for ACL tear classification with k = 40 support samples on the MRNet dataset). External validation on the KneeMRI dataset revealed challenges in classifying partially torn ACL (AUC up to 0.58) but demonstrated promising performance for distinguishing intact versus fully ruptured ACLs (AUC 0.62 with k = 40). Conclusions: These findings demonstrate that tailored FSL strategies can substantially reduce data dependency in developing specialized medical imaging tools. This approach fosters rapid AI tool development for knee injuries and offers a scalable solution for data scarcity in other medical imaging domains, potentially democratizing AI-assisted diagnostics, particularly for rare conditions or in resource-limited settings.