Using Large Binocular Telescope deep imaging data from the Smallest Scale of Hierarchy Survey (SSH) and archival Hubble Space Telescope data, we reveal the presence of two elongated stellar features contiguous to a bar-like stellar structure in the inner regions of the dwarf irregular galaxy NGC 3741. These structures are dominated by stars younger than a few hundred Myr and collectively are about twice as extended as the old stellar component. These properties are very unusual for dwarf galaxies in the nearby Universe and difficult to explain by hydro-dynamical simulations. From the analysis of archival 21-cm observations, we find that the young stellar "bar" coincides with an HI high-density region proposed by previous studies to be a purely gaseous bar; we furthermore confirm radial motions of a few km/s, compatible with an inflow/outflow, and derive a steeply-rising rotation curve and high HI surface density at the center, indicating a very concentrated mass distribution. We propose that the peculiar properties of the stellar and gaseous components of NGC 3741 may be explained by a recent merger or ongoing gas accretion from the intergalactic medium, which caused gas inflows towards the galaxy center and triggered star formation a few hundred Myr ago. This event may explain the young and extended stellar features, the bar-like structure, the very extended HI disc and the central HI spiral arms. The high central HI density and the steeply rising rotation curve suggest that NGC 3741 may be the progenitor or the descendant of a starburst dwarf.