On-device machine learning (ML) inference can enable the use of private user data on user devices without revealing them to remote servers. However, a pure on-device solution to private ML inference is impractical for many applications that rely on embedding tables that are too large to be stored on-device. In particular, recommendation models typically use multiple embedding tables each on the order of 1-10 GBs of data, making them impractical to store on-device. To overcome this barrier, we propose the use of private information retrieval (PIR) to efficiently and privately retrieve embeddings from servers without sharing any private information. As off-the-shelf PIR algorithms are usually too computationally intensive to directly use for latency-sensitive inference tasks, we 1) propose novel GPU-based acceleration of PIR, and 2) co-design PIR with the downstream ML application to obtain further speedup. Our GPU acceleration strategy improves system throughput by more than $20 \times$ over an optimized CPU PIR implementation, and our PIR-ML co-design provides an over $5 \times$ additional throughput improvement at fixed model quality. Together, for various on-device ML applications such as recommendation and language modeling, our system on a single V100 GPU can serve up to $100,000$ queries per second -- a $>100 \times$ throughput improvement over a CPU-based baseline -- while maintaining model accuracy.