Abstract Detection of gravitational waves (GWs) from neutron star-black hole (NSBH) standard sirens provides local measurements of the Hubble constant (H ₀), regardless of the detection of an electromagnetic (EM) counterpart, given that matter effects can be exploited to break the redshift degeneracy of the GW waveforms. The distinctive merger morphology and the high-redshift detectability of tidally disrupted NSBH make them promising candidates for this method. Also, the detection prospects of an EM counterpart for these systems will be limited to z < 0.8 in the optical, in the era of future GW detectors. Using recent constraints on the equation of state of NSs from multi-messenger observations of NICER and LIGO/Virgo/KAGRA, we show the prospects of measuring H ₀ solely from GW observation of NSBH systems, achievable by the Einstein telescope (ET) and Cosmic Explorer (CE) detectors. We first analyze individual events to quantify the effect of high-frequency (≥500 Hz) tidal distortions on the inference of NS tidal deformability parameter (Λ) and hence on H ₀. We find that disruptive mergers can constrain Λ up to  ( 60 % ) more precisely than nondisruptive ones. However, this precision is not sufficient to place stringent constraints on the H ₀ from individual events. By performing Bayesian analysis on simulated NSBH data (up to N = 100 events, corresponding to a day of observation) in the ET+CE detectors, we find that NSBH systems enable unbiased 4%–13% precision on the estimate of H ₀ (68% credible interval). This is a similar measurement precision found in studies analyzing NSBH mergers with EM counterparts in the LVKC O5 era.