An increasingly prevalent problem for intelligent technologies is text safety, as uncontrolled systems may generate recommendations to their users that lead to injury or life-threatening consequences. However, the degree of explicitness of a generated statement that can cause physical harm varies. In this paper, we distinguish types of text that can lead to physical harm and establish one particularly underexplored category: covertly unsafe text. Then, we further break down this category with respect to the system's information and discuss solutions to mitigate the generation of text in each of these subcategories. Ultimately, our work defines the problem of covertly unsafe language that causes physical harm and argues that this subtle yet dangerous issue needs to be prioritized by stakeholders and regulators. We highlight mitigation strategies to inspire future researchers to tackle this challenging problem and help improve safety within smart systems.