Foundation models (FMs) adapt well to specific domains or tasks with fine-tuning, and federated learning (FL) enables the potential for privacy-preserving fine-tuning of the FMs with on-device local data. For federated fine-tuning of FMs, we consider the FMs with small to medium parameter sizes of single digit billion at maximum, referred to as on-device FMs (ODFMs) that can be deployed on devices for inference but can only be fine-tuned with parameter efficient methods. In our work, we tackle the data and system heterogeneity problem of federated fine-tuning of ODFMs by proposing a novel method using heterogeneous low-rank approximations (LoRAs), namely HetLoRA. First, we show that the naive approach of using homogeneous LoRA ranks across devices face a trade-off between overfitting and slow convergence, and thus propose HetLoRA, which allows heterogeneous ranks across client devices and efficiently aggregates and distributes these heterogeneous LoRA modules. By applying rank self-pruning locally and sparsity-weighted aggregation at the server, HetLoRA combines the advantages of high and low-rank LoRAs, which achieves improved convergence speed and final performance compared to homogeneous LoRA. Furthermore, HetLoRA offers enhanced computation efficiency compared to full fine-tuning, making it suitable for federated fine-tuning across heterogeneous devices.