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We investigated the pressure-dependent exciton absorption and photoluminescence (PL) properties of colloidal InAs/ZnSe core/shell quantum dots (QDs) emitting near-infrared (NIR) photons, an environmentally friendly alternative to heavy-metal-containing NIR QDs. A detailed analysis of exciton absorption and emission spectra was conducted in the pressure range of 0–10 GPa, focusing on the energy shifts, PL intensity, and lineshape changes with pressure. The pressure coefficients for exciton absorption and PL peaks were ∼70% of the bulk InAs value, with enhanced bandgap nonlinearity tentatively attributed to the higher bulk modulus of QDs compared to bulk material. The pressure-induced shifts in exciton absorption and PL peaks were reversible upon compression and decompression, with no indication of the semiconductor-to-metallic phase transition observed in bulk InAs around 7 GPa. However, PL intensity exhibited partial irreversibility, suggesting defect formation at the core/shell interface under pressure. From the findings of this study, along with previous high-pressure studies on molecular beam epitaxy-grown InAs QDs on GaAs, we infer the importance of the shell in determining the pressure response of exciton absorption and PL in core/shell QD structures with non-negligible interfacial strain and wave function spill into the shell.