Aims. We study the variability of the Fe 6.4 keV emission line from the Class I young stellar object Elias 29 in the ρ Oph cloud. Methods. We analysed the data from Elias 29 collected by XMM-Newton during a nine-day, nearly continuous observation of the ρ Oph star-forming region (the Deep Rho-Oph X-ray Observation, named droxo). The data were subdivided into six homogeneous time intervals, and the six resulting spectra were individually analysed. Results. We detect significant variability in the equivalent width of the Fe 6.4 keV emission line from Elias 29. The 6.4 keV line is absent during the first time interval of observation and appears at its maximum strength during the second time interval (90 ks after Elias 29 undergoes a strong flare). The X-ray thermal emission is unchanged between the two observation segments, while line variability is present at a 99.9% confidence level. Given the significant line variability in the absence of variations in the X-ray ionising continuum and the weakness of the photoionising continuum from the star's thermal X-ray emission, we suggest that the fluorescence may be induced by collisional ionisation from an (unseen) population of non-thermal electrons. We speculate on the possibility that the electrons are accelerated in a reconnection event of a magnetically confined accretion loop, connecting the young star to its circumstellar disk.