We report the possible detection (99.3% of statistical significance) of redshifted iron line emission in the X-ray afterglow of gamma-ray burst GRB 970508 observed by BeppoSAX. Its energy is consistent with the redshift of the putative host galaxy determined from optical spectroscopy. The line disappeared ~1 day after the burst. We have also analyzed the spectral variability during the outburst event that characterizes the X-ray afterglow of this gamma-ray burst. The spectrum gets harder during the flare, then becoming steep when the flux decreases. The variability, intensity, and width of the line indicate that the emitting region should have a mass ≳0.5 M☉ (assuming that the iron abundance is similar to its solar value), should have a size of ~3×1015 cm, is distributed anisotropically, and is moving with subrelativistic speed. In contrast to the fairly clean environment expected in the merging of two neutron stars, the observed line properties would imply that the site of the burst is embedded in a large mass of material, consistent with preexplosion ejecta of a very massive star. This material could be related with the outburst observed in the afterglow 1 day after the GRB and with the spectral variations measured during this phase.