Dark matter may be in the form of non-baryonic structures such as compact subhalos and boson stars. Structures weighing between asteroid and solar masses may be discovered via gravitational microlensing, an astronomical probe that has in the past helped constrain the population of primordial black holes and baryonic MACHOs. We investigate the non-trivial effect of the size of and density distribution within these structures on the microlensing signal, and constrain their populations using the EROS-2 and OGLE-IV surveys. Structures larger than a solar radius are generally constrained more weakly than point-like lenses, but stronger constraints may be obtained for structures with mass distributions that give rise to caustic crossings or produce larger magnifications.