It is shown that in GaN/AlN multiple quantum wells (MQWs), strain is a critical parameter for achieving short-wavelength intersubband transitions (ISBTs). This is investigated by comparing GaN/AlN MQWs grown by metal organic vapor phase epitaxy on either AlN or GaN templates. The GaN/AlN interface is found to be unstable when pseudomorphically strained onto GaN, in agreement with theory. This effect deeply affects the quantum well potential profile leading to a strong redshift of the ISBT energies.