Recent advances in vision-language models (VLMs) have led to improved performance on tasks such as visual question answering and image captioning. Consequently, these models are now well-positioned to reason about the physical world, particularly within domains such as robotic manipulation. However, current VLMs are limited in their understanding of the physical concepts (e.g., material, fragility) of common objects, which restricts their usefulness for robotic manipulation tasks that involve interaction and physical reasoning about such objects. To address this limitation, we propose PhysObjects, an object-centric dataset of 39.6K crowd-sourced and 417K automated physical concept annotations of common household objects. We demonstrate that fine-tuning a VLM on PhysObjects improves its understanding of physical object concepts, including generalization to held-out concepts, by capturing human priors of these concepts from visual appearance. We incorporate this physically grounded VLM in an interactive framework with a large language model-based robotic planner, and show improved planning performance on tasks that require reasoning about physical object concepts, compared to baselines that do not leverage physically grounded VLMs. We additionally illustrate the benefits of our physically grounded VLM on a real robot, where it improves task success rates. We release our dataset and provide further details and visualizations of our results at https://iliad.stanford.edu/pg-vlm/.