  We report first constraints on neutrino electromagnetic properties 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$_\mathrm{th}$ reactor core of the Brokdorf nuclear
power plant in Germany. The CONUS low background detectors are positioned at
17.1 m distance from the reactor core center. The analyzed data set includes
689.1 kg$\cdot$d collected during reactor ON periods and 131.0 kg$\cdot$d
collected during reactor OFF periods in the energy range of 2 to 8 keV$_{ee}$.
With the current statistics, we are able to determine an upper limit on the
effective neutrino magnetic moment $\mu_\nu < 7.5\cdot10^{-11}\,\mu_B$ at 90%
confidence level. From this first magnetic moment limit we can derive an upper
bound on the neutrino millicharge of $\vert q_{\nu}\vert <
3.3\cdot10^{-12}\,e_0$.
