ABSTRACT The emission from the relativistic jets in blazars usually outshines their host galaxies, challenging the determination of their distances and the characterization of the stellar population. The situation becomes more favourable in the case of the extreme blazars (EHBLs), for which the bulk of the emission of the relativistic jets is emitted at higher energies, unveiling the optical emission from the host galaxy. The distance determination is fundamental for the study of the intrinsic characteristics of the blazars, especially to estimate the intrinsic gamma-ray spectra distorted due to the interaction with the extragalactic background light. In this work, we report on the properties of 2WHSP J073326.7+515354 host galaxy in the optical band, which is one of the few EHBLs detected at TeV energies. We present the first measurement of the distance of the source, z = 0.065 04 ± 0.000 02 (velocity dispersion $\sigma =237 \pm 9\, \mathrm{km s^{-1}}$). We also perform a detailed study of the stellar population of its host galaxy. We find that the mass-weighted mean stellar age is $11.72\pm 0.06\, \mathrm{Gyr}$ and the mean metallicity M/H = 0.159 ± 0.016. In addition, a morphological study of the host galaxy is also carried out. The surface brightness distribution is modelled by a composition of a dominant classical bulge (Re = 3.77 ± 1 arcsec or equivalently 4.74 kpc) plus an unresolved source which corresponds to the active nucleus. The black hole mass is estimated using both the mass relation with the velocity dispersion and the absolute magnitude from the bulge yielding comparable results: $(4.8\pm 0.9)\times 10^8$ and $(3.7\pm 1.0)\times 10^8\, \mathrm{ M}_{\odot }$, respectively.