We present new observations of the near-infrared hydrogen recombination lines Pa beta and Br gamma in the central starburst regions of 13 galaxies. The near-infrared data are supplemented with data on the optical Balmer line emission and are used to study the geometrical distribution of the dust associated with the massive stars. We find that the reddening toward the starburst regions can be explained by the presence of foreground dust, either homogeneous or clumpy. The result suggests that there is little internal dust in the star-forming site. Mechanisms like shock waves and outflows produced by supernova explosions and hot star winds can be effective at destroying and removing the dust from inside the region.