Ultra-luminous infrared galaxies (ULIRGs) have total infrared luminosities that exceed 10 12 solar luminosities, making them the most luminous objects in the infrared sky. They are mainly powered by starbursts with star-formation rates exceeding 100 solar masses per year, with a possible secondary contribution from an active galactic nucleus (AGN). Both starburst regions and AGN are environments in which hadronic acceleration, and hence neutrino production, is plausible. In this work we present the results of a stacking search for high-energy neutrinos from a representative sample of 75 local ULIRGs using 7.5 years of IceCube data. No significant neutrino excess is found. We therefore report upper limits on the neutrino flux originating from these 75 ULIRGs, and extrapolate these to limits on the full ULIRG source population. We also compare these results with model predictions.