Out-of-distribution (OOD) detection is crucial for the safe deployment of neural networks. Existing CLIP-based approaches perform OOD detection by devising novel scoring functions or sophisticated fine-tuning methods. In this work, we propose SeTAR, a novel, training-free OOD detection method that leverages selective low-rank approximation of weight matrices in vision-language and vision-only models. SeTAR enhances OOD detection via post-hoc modification of the model's weight matrices using a simple greedy search algorithm. Based on SeTAR, we further propose SeTAR+FT, a fine-tuning extension optimizing model performance for OOD detection tasks. Extensive evaluations on ImageNet1K and Pascal-VOC benchmarks show SeTAR's superior performance, reducing the relatively false positive rate by up to 18.95\% and 36.80\% compared to zero-shot and fine-tuning baselines. Ablation studies further validate our approach's effectiveness, robustness, and generalizability across different model backbones. Our work offers a scalable, efficient solution for OOD detection, setting a new state-of-the-art in this area.