We present an analysis of electron recoils in cryogenic germanium detectors operated during the SuperCDMS Soudan experiment. The data are used to set new constraints on the axioelectric coupling of axion-like particles and the kinetic mixing parameter of dark photons, assuming the respective species constitutes all of the galactic dark matter. This study covers the mass range from 40 eV/$c^2$ to 500 eV/$c^2$ for both candidates, excluding previously untested parameter space for masses below ~1 keV/$c^2$. For the kinetic mixing of dark photons, values below $10^{-15}$ are reached for particle masses around 100 eV/$c^2$; for the axioelectric coupling of axion-like particles, values below $10^{-12}$ are reached for particles with masses in the range of a few-hundred eV/$c^2$.