  This article reports the measurement of the ionization quenching factor in
germanium for nuclear recoil energies between 0.4 and 6.3 keV$_{nr}$. Precise
knowledge of this factor in this energy range is relevant for coherent elastic
neutrino-nucleus scattering and low mass dark matter searches with
germanium-based detectors. Nuclear recoils were produced in a thin high-purity
germanium target with a very low energy threshold via irradiation with
monoenergetic neutron beams. The energy dependence of the ionization quenching
factor was directly measured via kinematically constrained coincidences with
surrounding liquid scintillator based neutron detectors. The systematic
uncertainties of the measurements are discussed in detail. With measured
quenching factors between 0.16 and 0.23 in the [0.4, 6.3] keV$_{nr}$ energy
range, the data are compatible with the Lindhard theory with a parameter $k$ of
0.162 $\pm$ 0.004 (stat+sys).
