We calculate defect levels of dangling bonds in germanium using hybrid density functionals. To validate our approach, we first consider the dangling bond in silicon finding two well-separated defect levels, in excellent correspondence with their experimental location. Application of our scheme to the dangling bond in germanium then yields two very close defect levels lying just above the valence band, consistent with the location of the experimentally determined charge neutrality level. The small correlation energy and the proximity to the valence band edge provide an explanation for the absence of clear defect signatures in electrical and electron spin resonance experiments.