We present a study of 41 dwarf galaxies hosting active massive black holes (BHs) using Hubble Space Telescope observations. The host galaxies have stellar masses in the range of $M_star sim 10^{8.5}-10^{9.5}~M_odot$ and were selected to host active galactic nuclei (AGNs) based on narrow emission line ratios derived from Sloan Digital Sky Survey spectroscopy. We find a wide range of morphologies in our sample including both regular and irregular dwarf galaxies. We fit the HST images of the regular galaxies using GALFIT and find that the majority are disk-dominated with small pseudobulges, although we do find a handful of bulge-like/elliptical dwarf galaxies. We also find an unresolved source of light in all of the regular galaxies, which may indicate the presence of a nuclear star cluster and/or the detection of AGN continuum. Three of the galaxies in our sample appear to be Magellanic-type dwarf irregulars and two galaxies exhibit clear signatures of interactions/mergers. This work demonstrates the diverse nature of dwarf galaxies hosting optically-selected AGNs. It also has implications for constraining the origin of the first BH seeds using the local BH occupation fraction at low masses -- we must account for the various types of dwarf galaxies that may host BHs.