Foundation Models (FMs) have revolutionized machine learning with their adaptability and high performance across tasks; yet, their integration into Federated Learning (FL) is challenging due to substantial communication overhead from their extensive parameterization. Current communication-efficient FL strategies, such as gradient compression, reduce bitrates to around $1$ bit-per-parameter (bpp). However, these approaches fail to harness the characteristics of FMs, with their large number of parameters still posing a challenge to communication efficiency, even at these bitrate regimes. In this work, we present DeltaMask, a novel method that efficiently fine-tunes FMs in FL at an ultra-low bitrate, well below 1 bpp. DeltaMask employs stochastic masking to detect highly effective subnetworks within FMs and leverage stochasticity and sparsity in client masks to compress updates into a compact grayscale image using probabilistic filters, deviating from traditional weight training approaches. Our comprehensive evaluations across various datasets and architectures demonstrate DeltaMask efficiently achieves bitrates as low as 0.09 bpp, enhancing communication efficiency while maintaining FMs performance, as measured on 8 datasets and 5 pre-trained models of various network architectures.