Abstract We present a detailed analysis of the X-ray/IR fast variability of the Black-Hole Transient GX 339-4 during its low/hard state in 2008 August. Thanks to simultaneous high time resolution observations made with the VLT and RXTE, we performed the first characterization of the subsecond variability in the near-infrared band – and of its correlation with the X-rays – for a low-mass X-ray binary, using both time- and frequency-domain techniques. We found a power-law correlation between the X-ray and infrared fluxes when measured on time-scales of 16 s, with a marginally variable slope, steeper than the one found on time-scales of days at similar flux levels. We suggest the variable slope – if confirmed – could be due to the infrared flux being a non-constant combination of both optically thin and optically thick synchrotron emission from the jet, as a result of a variable self-absorption break. From cross spectral analysis, we found an approximately constant infrared time lag of ≈0.1 s, and a very high coherence of ∼90 per cent on time-scales of tens of seconds, slowly decreasing towards higher frequencies. Finally, we report on the first detection of a linear rms–flux relation in the emission from a low-mass X-ray binary jet, on time-scales where little correlation is found between the X-rays and the jet emission itself. This suggests that either the inflow variations and jet IR emission are coupled by a non-linear or time-variable transform, or that the IR rms–flux relation is not transferred from the inflow to the jet, but is an intrinsic property of emission processes in the jet.