Photoluminescence measurements have been performed on a series of InGaN/GaN multiple quantum well (MQW) nanorod array structures in order to investigate the influence of a nanorod structure on longitudinal optical (LO) phonon-exciton interaction. The nanorod array structures were fabricated on InGaN/GaN MQW epi-wafers using a self-organised Ni nano-mask technique. Compared with their corresponding as-grown samples, all the nanorod structures exhibit a significant reduction in Huang-Rhys factor, indicating a reduced coupling between LO-phonon and exciton. This is attributed to strain relaxation as a result of being fabricated into nanorod structures. Our excitation power dependent measurements have demonstrated that the nanorod structures exhibit a clear reduction in efficiency droop at a high excitation power. This proves a theoretical prediction previously reported, namely, LO-phonon-exciton coupling contributes to an indirect Auger recombination, leading to the efficiency droop of InGaN/GaN based emitters. The nanorod structures offering a reduced phonon-exciton coupling can pave the way for reducing or eliminating efficiency droop, one of the major challenges in the field of III-nitride optoelectronics.