Detailed calculations of the infrared emission from collisionally heated dust in the Coma cluster are presented. The proposed model includes continuous dust injection from galaxies, grain destruction by sputtering, and transient grain heating by the hot plasma. The computed infrared fluxes are in agreement with the upper limits obtained from the IRAS. The calculations, and constraints implied by the IRAS observations, suggest that the intracluster dust in the central region of the cluster must be significantly depleted compared to interstellar abundances. The observed visual extinction can therefore not be attributed to the presence of dust in that region. Extinction due to cluster galaxies or their haloes is ruled out as well. The only alternative explanation is that the extinction is caused by dust at great distances from the cluster center.