Extreme high-energy-peaked BL Lac objects (EHBLs) are an emerging class of blazars. Their typical two-hump-structured spectral energy distribution (SED) peaks at higher energies with respect to conventional blazars. Multiwavelength (MWL) observations constrain their synchrotron peak in the medium to hard X-ray band. Their gamma-ray SED peaks above the GeV band, and in some objects it extends up to several TeV. Up to now, only a few EHBLs have been detected in the TeV gamma-ray range. In this paper, we report the detection of the EHBL 2WHSP J073326.7+515354, observed and detected during 2018 in TeV gamma rays with the MAGIC telescopes. The broad-band SED is studied within an MWL context, including an analysis of the Fermi-LAT data over 10 yr of observation and with simultaneous Swift-XRT, Swift-UVOT, and KVA data. Our analysis results in a set of spectral parameters that confirms the classification of the source as an EHBL. In order to investigate the physical nature of this extreme emission, different theoretical frameworks were tested to model the broad-band SED. The hard TeV spectrum of 2WHSP J073326.7+515354 sets the SED far from the energy equipartition regime in the standard one-zone leptonic scenario of blazar emission. Conversely, more complex models of the jet, represented by either a two-zone spine-layer model or a hadronic emission model, better represent the broad-band SED.