  Single crystals of EuNiGe$_3$ crystallizing in the non-centrosymmetric
BaNiSn$_3$-type structure have been grown using In flux, enabling us to explore
the anisotropic magnetic properties which was not possible with previously
reported polycrystalline samples. The EuNiGe$_3$ single crystalline sample is
found to order antiferromagnetically at 13.2 K as revealed from the magnetic
susceptibility, heat capacity and electrical resistivity data. The low
temperature magnetization M(H) is distinctly different for field parallel to
${ab}$-plane and $c$-axis; the ${ab}$-plane magnetization varies nearly
linearly with field before the occurrence of an induced ferromagnetic phase
(spin-flip) at 6.2 Tesla; on the other hand M(H) along the $c$-axis is
accompanied by two metamagnetic transitions followed by a spin-flip at 4.1 T. A
model including anisotropic exchange and dipole-dipole interactions reproduces
the main features of magnetization plots but falls short of full
representation. (H,T) phase diagrams have been constructed for the field
applied along the principal directions. From the $^{151}$Eu M\"{o}ssbauer
spectra, we determine that the 13.2 K transition leads to an incommensurate
antiferromagnetic intermediate phase followed by a transition near 10.5 K to a
commensurate antiferromagnetic configuration.
