Metaphor, as a higher-order cognitive mechanism, operates by mapping familiar concepts from the target domain onto abstract and ambiguous concepts in the source domain, facilitating human comprehension and adaptation to novel domains and dynamic environments. In the field of natural language processing (NLP), metaphor research has witnessed significant advancements, leading to the emergence of numerous studies leveraging knowledge-assisted models for metaphor detection. Empirical findings indicate that systems incorporating external knowledge outperform those that do not, achieving state-of-the-art results in recent studies. Building upon these developments, this paper provides a comprehensive survey of deep learning-based knowledge injection techniques for metaphor detection. It first systematically categorizes and generalizes the primary types of knowledge and the principles underlying knowledge injection. Subsequently, it reviews the datasets, evaluation metrics, and benchmark models employed in metaphor detection tasks. Finally, it discusses the key challenges associated with knowledge injection methods and outlines potential directions for future research.