With the advent of detectors with sub-keV sensitivities, atomic ionization has been identified as a promising avenue to probe possible neutrino electromagnetic properties. The interaction cross sections induced by millicharged neutrinos are evaluated with the ab initio multiconfiguration relativistic random-phase approximation. There is significant enhancement at atomic binding energies compared to that when the electrons are taken as free particles. Positive signals would distinctly manifest as peaks at specific energies with known intensity ratios. Selected reactor neutrino data with germanium detectors at an analysis threshold as low as 300 eV are studied. No such signatures are observed, and a combined limit on the neutrino charge fraction of |δQ|<1.0×10-12 at 90% confidence level is derived.