We analyze Hubble Space Telescope WFC3/H sub(160)-band observations of a sample of 48 Atacama Large Millimeter/submillimeter Array detected submillimeter galaxies (SMGs) in the Extended Chandra Deep Field South field, to study their stellar morphologies and sizes. We detect 79% + or - 17% of the SMGs in the H sub(160)-band imaging with a median sensitivity of 27.8 mag, and most (80%) of the nondetections are SMGs with 870 mu m fluxes of S sub(870) < 3 mJy. With a surface brightness limit of mu H ~26 mag arcsec super(-2), we find that 82% + or - 9% of the H sub(160)-band-detected SMGs at z = 1-3 appear to have disturbed morphologies, meaning they are visually classified as either irregulars or interacting systems, or both. By determining a Sersic fit to the H sub(160) surface brightness profiles, we derive a median Sersic index of n = 1.2 + or - 0.3 and a median half-light radius of re = (ProQuest: Formulae and/or non-USASCII text omitted) kpc for our SMGs at z = 1-3. We also find significant displacements between the positions of the H sub(160) component and 870 mu m emission in these systems, suggesting that the dusty starburst regions and less-obscured stellar distribution are not colocated. We find significant differences in the sizes and the Sersic index between our z = 2-3 SMGs and z ~ 2 quiescent galaxies, suggesting that a major transformation of the stellar light profile is needed in the quenching processes if SMGs are progenitors of the red-and-dead z ~ 2 galaxies. Given the short-lived nature of SMGs, we postulate that the majority of the z = 2-3 SMGs with S sub(870) > ~ 2 mJy are early/mid-stage major mergers.