Temporally modulated electron beams have a wide array of applications ranging from the generation of coherently enhanced electromagnetic radiation to the resonant excitation of electromagnetic wakefields in advanced-accelerator concepts. Likewise producing low-energy ultrashort microbunches could be useful for ultrafast electron diffraction and new accelerator-based light-source concepts. In this Letter we propose and experimentally demonstrate a passive microbunching technique capable of forming a picosecond bunch train at ∼6 MeV. The method relies on the excitation of electromagnetic wakefields as the beam propagates through a dielectric-lined waveguide. Owing to the nonultrarelativistic nature of the beam, the induced energy modulation eventually converts into a density modulation as the beam travels in a following free-space drift. The modulated beam is further accelerated to ∼20 MeV while preserving the imparted density modulation.