Abstract We present HaloFlow, a new machine-learning approach for inferring the mass of host dark matter halos, M _h , from the photometry and morphology of galaxies (https://github.com/changhoonhahn/haloflow/). HaloFlow uses simulation-based inference with normalizing flows to conduct rigorous Bayesian inference. It is trained on state-of-the-art synthetic galaxy images from Bottrell et al. that are constructed from the IllustrisTNG hydrodynamic simulation and include realistic effects of the Hyper Suprime-Cam Subaru Strategy Program observations. We design HaloFlow to infer M _h and stellar mass, M _*, using grizy band magnitudes, morphological properties quantifying characteristic size, concentration and asymmetry, total measured satellite luminosity, and number of satellites. We demonstrate that HaloFlow infers accurate and unbiased posteriors of M _h . Furthermore, we quantify the full information content in the photometric observations of galaxies in constraining M _h . With magnitudes alone, we infer M _h with σ log M h ∼ 0.115 and 0.182 dex for field and group galaxies. Including morphological properties significantly improves the precision of M _h constraints, as does total satellite luminosity: σ log M h ∼ 0.095 and 0.132 dex. Compared to the standard approach using the stellar-to-halo mass relation, we improve M _h constraints by ∼40%. In subsequent papers, we will validate and calibrate HaloFlow with galaxy–galaxy lensing measurements on real observational data.