We introduce Monarch Sparse Tuning (MoST), the first reparameterization-based parameter-efficient fine-tuning (PEFT) method for 3D representation learning. Unlike existing adapter-based and prompt-tuning 3D PEFT methods, MoST introduces no additional inference overhead and is compatible with any 3D representation learning backbone. At its core, we tailor a new family of structured matrices for 3D point clouds, Point Monarch, which can capture local geometric features of irregular points while offering high expressiveness. MoST reparameterizes the dense update weight matrices as our sparse Point Monarch matrices, significantly reducing parameters while retaining strong performance. Experiments on various backbones show that MoST is simple, effective, and highly generalizable. It captures local features in point clouds, achieving state-of-the-art results on multiple benchmarks, such as 97.5% acc. on ScanObjectNN (PB50RS) and 96.2% on ModelNet40 classification, while it can also combine with other matrix decompositions (e.g., Low-rank, Kronecker) to further reduce parameters.