Defect levels of dangling bonds in germanium are calculated through the use of hybrid density functionals. The theoretical approach is first validated through the consideration of the well-characterized defect levels of the dangling bond in silicon, for which two well-separated defect levels are found in excellent correspondence with their experimental location. For germanium, our scheme then yields two very close defect levels, located just above the valence band maximum. These findings are consistent with measurements of the charge neutrality level, lying within 0.1 eV from the valence band edge. The small correlation energy and the proximity to the valence band edge provide a rationale for the absence of clear defect signatures for germanium dangling bonds in electrical and electron-spin-resonance experiments.