We have grown single crystals of YbFe6Ge6 and LuFe6Ge6 and characterized their anisotropic behaviour through low field magnetic susceptibility, field-dependent magnetization, resistivity and heat capacity measurements. The Yb+3 valency is confirmed by LIII XANES measurements. YbFe6Ge6 crystals exhibit a field-dependent, sudden reorientation of the Fe spins at about 63 K, a unique effect in the RFe6Ge6 family (R = rare earths) where the Fe ions order anti-ferromagnetically with Neel temperatures above 450 K and the R ions magnetism appears to behave independently. The possible origins of this unusual behaviour of the ordered Fe moments in this compound are discussed.