We investigate the quantum size effects in the pressure-induced direct-to-indirect band gap transition in InP nanocrystals. Hydrostatic pressures of up to 13 GPa are applied to two different sizes of InP nanocrystal samples in a diamond anvil cell. The band gap pressure dependence and the nature of the emitting states are studied by photoluminescence (PL) and fluorescence line narrowing (FLN) techniques at 10 K. Pressure-dependent FLN spectra show that the nature of the emitting states at pressures up to 9 GPa is similar to that at ambient pressure, suggesting that no direct-to-indirect transition happens below 9 GPa. For both sizes, the PL peak energy exhibits a strong blueshift with rising pressure until approximately 9 to 10 GPa. Above this pressure, the PL peak position slightly shifts red. Beyond 12 GPa, the band gap emission intensity becomes extremely weak and trap emission dominates the PL spectra. As the pressure is released, both the luminescence intensity and the peak position recover in a fully reversible manner. The change in the sign of the band gap energy pressure dependence and the disappearance of the band edge luminescence indicate the pressure-induced direct-to-indirect band gap transition. Contrary to theoretical calculations, no substantial reduction of the transition pressure is observed in the nanocrystal cases compared to the bulk transition pressure.