Impulsive stimulated light scattering and Raman spectroscopy measurements have been made on hcp cobalt to a static pressure of 120 GPa. We find that at pressures above 60 GPa the shear elastic modulus and the Raman frequency of the E(2g) transverse optical phonon exhibit a departure from a linear dependence on density. We relate this behavior to a collapse of the magnetic moment under pressure that has been predicted theoretically, but until now not observed experimentally.