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 ( \sigma _ { * } < 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 \lesssim 10 ^ { 6 } M _ { \odot } . Three out of four objects were detected with > 3 \sigma significance in \sim 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 \Gamma = 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 } ~ { } \sim~ { } 10 ^ { 22 } ~ { } { 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 _ { \mathrm { bol } } \sim 10 ^ { 40 } -10 ^ { 41 } erg s ^ { -1 } .