High pressure X-ray diffraction measurements have been carried out on the intermetallic semiconductor FeGa$_3$ and the equation of state for FeGa$_3$ has been determined. First principles based DFT calculations within the GGA approximation indicate that although the unit cell volume matches well with the experimentally obtained value at ambient pressure, it is significantly underestimated at high pressures and the difference between them increases as pressure increases. GGA + U calculations with increasing values of U$_{Fe(3d)}$ (on-site Coulomb repulsion between the Fe 3d electrons) at high pressures, correct this discrepancy. Further, the GGA+U calculations also show that along with U$_{Fe(3d)}$, the Fe 3d band width also increases with pressure and around a pressure of 4 GPa, a small density of states appear at the Fermi level. High pressure resistance measurements carried out on FeGa$_3$ also clearly show a signature of an electronic transition. Beyond the pressure of 19.7 GPa, the diffraction peaks reduce in intensity and are not observable beyond $sim$ 26 GPa, leading to an amorphous state.
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