We have examined the physical conditions in the narrow-line region (NLR) of the Seyfert 2 galaxy Markarian 3, using long-slit spectra obtained with the Hubble Space Telescope/Space Telescope Imaging Spectrograph and photoionization models. We find three components of photoionized gas in the NLR. Two of these components, characterized by emission lines such as [NeV] 3426 and [OIII] 5007, lie within the envelope of the bi-conical region described in our previous kinematic study. A component of lower ionization gas, in which lines such as [OII] 3727 arise, is found to lie outside the bi-cone. Each of these components is irradiated by a power-law continuum which is attenuated by intervening gas, presumably closer to the central source. The radiation incident upon the low ionization gas, external to the bi-cone, is much more heavily absorbed. These absorbers are similar to the intrinsic UV and X-ray absorbers detected in many Seyfert 1 galaxies, which suggests that the collimation of the ionizing radiation occurs in a circumnuclear wind, rather than a thick, molecular torus. We estimate the mass for the observed NLR emitting gas to be 2 million solar-masses. It is likely that Markarian 3 acquired this gas through an on-going interaction with the spiral galaxy UGC 3422.