We report first constraints on electromagnetic properties of neutrinos from neutrino-electron scattering using data obtained from the CONUS germanium detectors, i.e. an upper limit on the effective neutrino magnetic moment and an upper limit on the effective neutrino millicharge. The electron antineutrinos are emitted from the 3.9  GW th reactor core of the Brokdorf Nuclear Power Plant in Germany. The CONUS low-background detectors are positioned at a distance of 17.1 m from the reactor core center. The analyzed data set includes 689.1 kg d collected during reactor ON periods and 131.0 kg d collected during reactor OFF periods in the energy range of . With the current statistics, we are able to determine an upper limit on the effective neutrino magnetic moment of μ ν < 7.5 · 10 - 11 μ B at 90% confidence level. No neutrino signal in this channel or in the CE ν NS channel has been observed at a nuclear power plant so far. From this first magnetic moment limit we can derive an upper bound on the neutrino millicharge of | q ν | < 3.3 · 10 - 12 e 0 .