N-ary Knowledge Graphs (NKGs) are a specialized type of knowledge graph designed to efficiently represent complex real-world facts. Unlike traditional knowledge graphs, where a fact typically involves two entities, NKGs can capture n-ary facts containing more than two entities. Link prediction in NKGs aims to predict missing elements within these n-ary facts, which is essential for completing NKGs and improving the performance of downstream applications. This task has recently gained significant attention. In this paper, we present the first comprehensive survey of link prediction in NKGs, providing an overview of the field, systematically categorizing existing methods, and analyzing their performance and application scenarios. We also outline promising directions for future research.