Quantum autoencoders serve as efficient means for quantum data compression. Here, we propose and demonstrate their use to reduce resource costs for quantum teleportation of subspaces in high-dimensional systems. We use a quantum autoencoder in a compress-teleport-decompress manner and report the first demonstration with qutrits using an integrated photonic platform for future scalability. The key strategy is to compress the dimensionality of input states by erasing redundant information and recover the initial states after chip-to-chip teleportation. Unsu-pervised machine learning is applied to train the on-chip autoencoder, enabling the compression and teleportation of any state from a high-dimensional subspace. Unknown states are decompressed at a high fidelity (-0.971), obtain-ing a total teleportation fidelity of-0.894. Subspace encodings hold great potential as they support enhanced noise robustness and increased coherence. Laying the groundwork for machine learning techniques in quantum systems, our scheme opens previously unidentified paths toward high-dimensional quantum computing and networking.