We present XMM-Newton observations of four low-redshift Seyfert galaxies selected to have low host luminosities (M_g > – 20 mag) and small stellar velocity dispersions (σ_* <45 km s^–1), which are among the smallest stellar velocity dispersions found in any active galaxies. These galaxies show weak or no broad optical emission lines and have likely black hole masses 10⁶ M _☉. Three out of four objects were detected with >3σ significance in ~25 ks exposures and two observations had high enough signal-to-noise ratios for rudimentary spectral analysis. We calculate hardness ratios (–0.43 to 0.01) for the three detected objects and use them to estimate photon indices in the range of Γ = 1.1-1.8. Relative to [O III], the type 2 objects are X-ray faint in comparison with Seyfert 1 galaxies, suggesting that the central engines are obscured. We estimate the intrinsic absorption of each object under the assumption that the [O III] emission line luminosities are correlated with the unabsorbed X-ray luminosity. The results are consistent with moderate (N _H ~ 10²² cm^-2) absorption over the Galactic values in three of the four objects, which might explain the non-detection of broad-line emission in optical spectra. One object in our sample, SDSS J110912.40+612346.7, is a near identical type 2 counterpart of the late-type Seyfert 1 galaxy NGC 4395. While the two objects have very similar [O III] luminosities, the type 2 object has an X-ray/[O III] flux ratio nearly an order of magnitude lower than NGC 4395. The most plausible explanation for this difference is absorption of the primary X-ray continuum of the type 2 object, providing an indication that obscuration-based unified models of active galaxies can apply even at the lowest luminosities seen among Seyfert nuclei, down to L _bol ~10⁴⁰-10⁴¹ erg s^–1.