More music foundation models are recently being released, promising a general, mostly task independent encoding of musical information. Common ways of adapting music foundation models to downstream tasks are probing and fine-tuning. These common transfer learning approaches, however, face challenges. Probing might lead to suboptimal performance because the pre-trained weights are frozen, while fine-tuning is computationally expensive and is prone to overfitting. Our work investigates the use of parameter-efficient transfer learning (PETL) for music foundation models which integrates the advantage of probing and fine-tuning. We introduce three types of PETL methods: adapter-based methods, prompt-based methods, and reparameterization-based methods. These methods train only a small number of parameters, and therefore do not require significant computational resources. Results show that PETL methods outperform both probing and fine-tuning on music auto-tagging. On key detection and tempo estimation, they achieve similar results as fine-tuning with significantly less training cost. However, the usefulness of the current generation of foundation model on key and tempo tasks is questioned by the similar results achieved by training a small model from scratch. Code available at https://github.com/suncerock/peft-music/