ABSTRACT We report the detection of an infrared burst lagging a thermonuclear Type I X-ray burst from the accreting neutron star (NS) 4U 1728-34 (GX 354-0). Observations were performed simultaneously with XMM–Newton (0.7–12 keV), NuSTAR (3–79 keV), and HAWK-I@VLT (2.2 $\, μ$m). We measure a lag of 4.75 ± 0.5 s between the peaks of the emission in the two bands. Due to the length of the lag and the shape of the IR burst, we found that the most plausible cause for such a large delay is reprocessing of the Type I burst X-rays by the companion star. The inferred distance between the NS and the companion can be used to constrain the orbital period of the system, which we find to be larger than ∼66 min (or even ≳2 h, for a realistic inclination <75°). This is much larger than the current tentatively estimated period of ∼11 min. We discuss the physical implications on the nature of the binary and conclude that most likely the companion of 4U 1728-34 is a helium star.