The Cryogenic Dark Matter Search low ionization threshold experiment (CDMSlite) achieved efficient detection of very small recoil energies in its germanium target, resulting in sensitivity to lightly ionizing particles (LIPs) in a previously unexplored region of charge, mass, and velocity parameter space. We report first direct-detection limits calculated using the optimum interval method on the vertical intensity of cosmogenically produced LIPs with an electric charge smaller than e/(3×105), as well as the strongest limits for charge ≤e/160, with a minimum vertical intensity of 1.36×10−7 cm−2 s−1 sr−1 at charge e/160. These results apply over a wide range of LIP masses (5 MeV/c2 to 100 TeV/c2) and cover a wide range of βγ values (0.1–106), thus excluding nonrelativistic LIPs with βγ as small as 0.1 for the first time.