We present deep Hubble Space Telescope (HST) imaging, as well as ground-based imaging and spectroscopy, of the optical afterglow associated with the long-duration gamma-ray burst GRB 990712 and its host galaxy. The data were obtained 48-123 days after the burst occurred. The magnitudes of the host (R=21.9, V=22.5) and optical afterglow (R=25.4, V=25.8, 47.7 days after the burst) favor a scenario in which the optical light follows a pure power-law decay with an index of alpha approximately -1.0. We find no evidence for a contribution from a supernova like SN 1998bw. This suggests that either there are multiple classes of long-duration gamma-ray bursts or that the peak luminosity of the supernova was more than 1.5 mag fainter than SN 1998bw. The HST images and EFOSC2 spectra indicate that the gamma-ray burst was located in a bright, extended feature (possibly a star-forming region) 1.4 kpc from the nucleus of a 0.2L*B galaxy at z=0.434, possibly a Seyfert 2 galaxy. The late-time afterglow and host galaxy of GRB 990712 bear some resemblance to those of GRB 970508.