We report on the exchange biasing of self-assembled ferromagnetic GeMn nanocolumns by GeMn-oxide caps. The x-ray absorption spectroscopy analysis of this surface oxide shows a multiplet fine structure that is typical of the Mn2+ valence state in MnO. A magnetization hysteresis shift |HE|~100 Oe and a coercivity enhancement of about 70 Oe have been obtained upon cooling (300-5 K) in a magnetic field as low as 0.25 T. This exchange bias is attributed to the interface coupling between the ferromagnetic nanocolumns and the antiferromagnetic MnO-like caps. The effect enhancement is achieved by depositing a MnO layer on the GeMn nanocolumns.