The effect of hydrostatic pressure on optical transitions in InGaN/GaN multiple quantum wells (MQWs) has been studied. Photoluminescence (PL) and photomodulated transmission (PT) measurements were performed under applied pressure to examine the pressure dependence of optical transitions associated with confined states in MQWs. The PL emission from the MQWs was found to shift linearly to higher energy with applied pressure but exhibit a significantly weaker pressure dependence compared to epilayer samples with similar bandgap energies. Similar pressure coefficients obtained by PT measurements rule out the possibility of PL resulting from deep localized states. We show that the difference in the compressibility of InGaN and of GaN induces a tensile strain in the compressively strained InGaN well layers that partially compensates the applied hydrostatic pressure. This mechanical effect is the primary factor for the smaller pressure dependence of the optical transitions in the InGaN/GaN MQWs. At pressure above 100 kbar, the PL signal in MQWs samples is quenched, indicating that the carriers involved in the radiative recombination processes in the well layers originate primarily from the adjacent GaN layers.