We report near-infrared and optical follow-up observations of the afterglow of the GRB 000418 starting 2.5 days after the occurrence of the burst and extending over nearly 7 weeks. GRB 000418 represents the second case for which the afterglow was initially identified by observations in the near-infrared. During the first 10 days its R-band afterglow was well characterized by a single power-law decay with a slope of 0.86. However, at later times the temporal evolution of the afterglow flattens with respect to a simple power-law decay. Attributing this to an underlying host galaxy, we find its magnitude to be R=23.9 and an intrinsic afterglow decay slope of 1.22. The afterglow was very red with R-K~4 mag. The observations can be explained by an adiabatic, spherical fireball solution and a heavy reddening due to dust extinction in the host galaxy. This supports the picture that (long) bursts are associated with events in star-forming regions. Based on observations collected at the Bologna Astronomical Observatory in Loiano, Italy; at the TNG, Canary Islands, Spain; at the German-Spanish Astronomical Centre, Calar Alto, operated by the Max-Planck-Institut for Astronomy, Heidelberg, jointly with the Spanish National Commission for Astronomy; at the US Naval Observatory; and at the UK Infrared Telescope.