Compared to the in-air case, underwater depth estimation has its own challenges. For instance, acquiring high-quality training datasets with groundtruth poses difficulties due to sensor limitations in aquatic environments. Additionally, the physics characteristics of underwater imaging diverge significantly from the in-air case, the methods developed for in-air depth estimation underperform when applied underwater, due to the domain gap. To address these challenges, our paper introduces a novel transfer-learning-based method - Physics-informed Underwater Depth Estimation (\textbf{PUDE}). The key idea is to transfer the knowledge of a pre-trained in-air depth estimation model to underwater settings utilizing a small underwater image set without groundtruth measurement, guided by a physical model for underwater image formation. We propose novel bound losses based on the physical model to rectify the depth estimations to align with actual underwater physical properties. Finally, in the evaluations across multiple datasets, we compare our Physics-informed Underwater Depth Estimation (\textbf{PUDE}) model with other existing in-air and underwater methods. The results reveal that the \textbf{PUDE} model excels in both quantitative and qualitative comparisons.