We describe a sample of low-mass Seyfert 2 galaxies selected from the Sloan Digital Sky Survey (SDSS), with a median absolute magnitude of Mg = –19.0 mag. These galaxies are Type 2 counterparts to the Seyfert 1 galaxies with intermediate-mass black holes identified by Greene & Ho. Spectra obtained with the Echellette Spectrograph and Imager at the Keck Observatory are used to determine the central stellar velocity dispersions and to examine the emission-line properties. Overall, the stellar velocity dispersions are low (~40-90 km s–1), and we find 12 objects having σ < 60 km s–1, a range where very few Seyfert 2 galaxies were previously known. The sample follows the correlation between stellar velocity dispersion and FWHM([O III]) seen in more massive Seyfert galaxies, indicating that the narrow-line FWHM values are largely determined by virial motion of gas in the central regions of the host galaxies, but the [O III] emission lines exhibit a higher incidence of redward asymmetries and double-peaked profiles than what is found in typical Seyfert samples. Using estimates of the black hole masses and active galactic nucleus (AGN) bolometric luminosities, we find that these galaxies are typically radiating at a high fraction of their Eddington rate, with a median L bol/L Edd = 0.4. We identify one galaxy, SDSS J110912.40+612346.7, as a Type 2 analog of the nearby dwarf Seyfert 1 galaxy NGC 4395, with a nearly identical narrow-line spectrum and a dwarf spiral host of only Mg = –16.8 mag. The close similarities between these two objects suggest that the obscuring torus of AGN unification models may persist even at the lowest luminosities seen among Seyfert galaxies, below L bol = 1041 ergs s–1. Spectropolarimetry observations of four objects do not reveal any evidence for polarized broad-line emission, but SDSS J110912.40+612346.7 has a continuum polarization significantly in excess of the expected Galactic foreground polarization, a possible indication of scattered light from a hidden nucleus. Forthcoming observations of this sample, including X-ray and mid-infrared spectroscopy, can provide new tests of the obscuring torus model for active galaxies at low luminosities.