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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).