We have identified a new externally irradiated Herbig–Haro (HH) jet, HH 1158, within ~2 pc of the massive OB type stars in the σ Orionis cluster. At an Lbol ~ 0.1 L⊙, HH 1158 is the lowest luminosity irradiated HH jet identified to date in any cluster. Results from the analysis of high-resolution optical spectra indicate asymmetries in the brightness, morphology, electron density, velocity, and the mass outflow rates for the blue and redshifted lobes. We constrain the position angle of the HH 1158 jet at 102° ± 5°. The mass outflow rate and the mean accretion rate for HH 1158 using multiple diagnostics are estimated to be (5.2 ± 2.6) × 10−10 M⊙ yr−1 and (3.0 ± 1.0) × 10−10 M⊙ yr−1, respectively. The properties for HH 1158 are notably similar to the externally irradiated HH 444–HH 447 jets previously identified in σ Orionis. In particular, the morphology is such that the weaker jet beam is tilted toward the massive stars, indicating a higher extent of photo-evaporation. The high value for the Hα/[S ii] ratio is also consistent with the ratios measured in other irradiated jets, including HH 444–HH 447. The presence of an extended collimated jet that is bipolar and the evidence of shocked emission knots make HH 1158 the first unique case of irradiated HH jets at the very low-luminosity end, and provides an opportunity to learn the physical properties of very faint HH jet sources.