Geometrically frustrated Magnets continue to attract attention due to their inclination towards unconventional ground states at low temperatures. Among these, GeCo₂O₄ a normal spinel, has been recently suggested to undergo a magnetic ordering at 21K accompanied by a cubic-tetragonal distortion. However, its low temperature properties especially the nature and origin of the structural distortion are not clearly understood to date. Therefore we have investigated the elastic and magnetic properties of GeCo₂O₄ single crystal using ultrasound velocity measurements down to 2K. The temperature dependence of the elastic constant C₄₄, at zero magnetic field shows an anomaly at 20.8K consistent with a first order AF phase transition. The elastic instability of C₄₄ implies that, the magnetic ordering might be accompanied by a cubic-tetragonal distortion. When the field is applied along [100], the maximum critical field is 10.5T. For fields B// [111], the maximum critical fields of the first and second phase transition is 11T and 13T, respectively. Whereas for fields B// [110], the maximum critical fields of the first and second phase transition are 4.5T and 9.5T, respectively. The magnetic field anisotropy is probably due to distortion of the crystal lattice at higher magnetic fields.