We present the results of a near-infrared and X-ray study of the Seyfert 2 galaxy NGC 3281. Emission from the Seyfert nucleus is detected in both regions of the electromagnetic spectrum, allowing us to infer both the equivalent line of sight hydrogen column density, N=71.0+ 11.3−12.3×1026 m-2, and the extinction due to dust, AV = 22 ± 11 mag (90% confidence intervals). We infer a ratio of NH/AV that is an order of magnitude larger than that determined along lines of sight in the Milky Way and discuss possible interpretations. We consider the most plausible explanation to be a dense cloud in the foreground of both the X-ray and infrared-emitting regions that obscures the entire X-ray source but only a fraction of the much larger infrared source.