The bright submillimetre (sub-mm) galaxy MM 18423+5938 at redshift 3.9296 has been predicted from mid-infrared (MIR) and millimetre photometry to have an exceptionally large total IR luminosity. We present new radio imaging at 1.4 GHz with the Westerbork Synthesis Radio Telescope that is used to determine a radio-derived total IR luminosity for MM 18423+5938 via the well-established radio–far-IR correlation. The flux density is found to be S1.4 GHz= 217 ± 37 μJy, which corresponds to a rest-frame luminosity density of L1.4 GHz= 2.32 ± 0.40 × 1025μ−1 W Hz−1, where μ is the magnification from a probable gravitational lens. The radio-derived total IR luminosity and star formation rate are L8−1000 μm= 5.6+4.1−2.4× 1013 μ−1 L⊙ and SFR =9.4+7.4−4.9× 103 μ−1 M⊙ yr−1, respectively, which are ∼9 times smaller than those previously reported. These differences are attributed to the IR spectral energy distribution of MM 18423+5938 being poorly constrained by the limited number of reliable photometric data that are currently available, and from a previous misidentification of the object at 70 μm. Using the radio derived total IR luminosity as a constraint, the temperature of the cold dust component is found to be Td∼ 24+7−5 K for a dust emissivity of β= 1.5 ± 0.5. The radio-derived properties of this galaxy are still large given the low excitation temperature implied by the CO emission lines and the temperature of the cold dust. Therefore, we conclude that MM 18423+5938 is probably gravitationally lensed.