The intermetallic compound FeGa${}_{3}$ is a narrow-gap semiconductor with a measured gap between 0.2 and 0.6 eV. The presence of iron $d$ states on the top of the valence band and on the bottom of the conduction band, together with its moderate electronic correlation ($U/W\ensuremath{\sim}0.6$), have led to the question of whether there is magnetic order in this compound. We have examined the possible presence of magnetism in FeGa${}_{3}$ as well as its electronic structure at high pressures, using the density functional theory (DFT) $+$ $U$ method with the intermediated double-counting scheme. We have found that for an optimized value of the Yukawa screening length $\ensuremath{\lambda}$, there is no magnetic moment on the iron ions ($\ensuremath{\mu}=0$), implying that FeGa${}_{3}$ is nonmagnetic. We have also found that around a pressure of 25 GPa a metal-insulator transition takes place.