With the ubiquity of hyper-relational facts in modern Knowledge Graphs (KGs), existing link prediction techniques mostly focus on learning the sophisticated relationships among multiple entities and relations contained in a fact, while ignoring the multimodal information, which often provides additional clues to boost link prediction performance. Nevertheless, traditional multimodel fusion approaches, which are mainly designed for triple facts under either entity-centric or relation-guided fusion schemes, fail to integrate the multimodal information with the rich context of the hyper-relational fact consisting of multiple entities and relations. Against this background, we propose **HyperFM**, a **Hyper**-relational **F**act-centric **M**ultimodal Fusion technique. It effectively captures the intricate interactions between different data modalities while accommodating the hyper-relational structure of the KG in a fact-centric manner via a customized Hypergraph Transformer. We evaluate HyperFM against a sizeable collection of baselines in link prediction tasks on two real-world KG datasets. Results show that HyperFM consistently achieves the best performance, yielding an average improvement of 6.0-6.8% over the best-performing baselines on the two datasets. Moreover, a series of ablation studies systematically validate our fact-centric fusion scheme.