Observations at near and mid-infrared wavelengths (1-18 micron) of SGR 1806-20 suggest that it is associated with a cluster of giant massive stars which are enshrouded in a dense cloud of dust. The centre of the best sky position of the gamma-ray source (Hurley et al. 1999) lies on top of the dust cloud at only 7 arcsec (~0.5 pc at a distance of 14.5 kpc) from the star cluster, and 12 arcsec (~0.85 pc) from a Luminous Blue Variable Star (LBV) which had been proposed to be associated with the SGR (Kulkarni et al. 1995). The bright cloud of interstellar gas and dust observed with ISO (Infrared Space Observatory) is probably the birth site of the cluster of massive stars, the LBV star, and the progenitor of the soft gamma-ray repeater pulsar. The presence of such a young star formation region is compatible with the current interpretation of soft gamma-ray repeaters as young neutron stars. The SGR 1806-20 compact source is unlikely to form a bound binary system with any of the infrared luminous massive stars, since no flux variations in the near-infrared were detected from the latter in an interval of 4 years.The ISO observations were made over two epochs, 11 days before and 2 hours after a soft gamma-ray burst detected with the Interplanetary Network, and they show no enhanced mid-infrared emission associated to the high energy activity of the SGR.