We present JWST/MIRI spectra from the Medium-Resolution Spectrometer of I Zw 18, a nearby dwarf galaxy with a metallicity of ∼3% solar. Its proximity enables a detailed study of highly ionized gas that can be interpreted in the context of newly discovered high-redshift dwarf galaxies. We derive aperture spectra centered on 11 regions of interest; the spectra show very low extinction, A_V ≲ 0.1, consistent with optical determinations. The gas is highly ionized; we have detected 10 fine-structure lines, including [O IV] 25.9 μm with an ionization potential (IP) of ∼55 eV, and [Ne V] 14.3 μm with an IP of ∼97 eV. The ionization state of I Zw 18 falls at the extreme upper end of all of the line ratios we analyzed, but not coincident with galaxies containing an accreting massive black hole (active galactic nucleus). Comparison of the line ratios with state-of-the-art photoionization and shock models suggests that the high-ionization state in I Zw 18 is not due to shocks. Rather, it can be attributed to metal-poor stellar populations with a self-consistent contribution of X-ray binaries or ultra-luminous X-ray sources. It could also be partially due to a small number of hot low-metallicity Wolf−Rayet stars ionizing the gas; a small fraction (a few percent) of the ionization could come from an intermediate-mass black hole. Our spectroscopy also revealed four 14 μm continuum sources, ≳30–100 pc in diameter, three of which were not previously identified. Their properties are consistent with H II regions ionized by young star clusters.