Different approaches to quantum gravity, such as string theory and loop quantum gravity, as well as doubly special relativity and gedanken experiments in black-hole physics, all indicate the existence of a minimal measurable length7, 8 of the order of the Planck length, . This observation has motivated the proposal of generalized uncertainty relations, which imply changes in the energy spectrum of quantum systems. As a consequence, quantum gravitational effects could be revealed by experiments able to test deviations from standard quantum mechanics, such as those recently proposed on macroscopic mechanical oscillators12. Here we exploit the sub-millikelvin cooling of the normal modes of the ton-scale gravitational wave detector AURIGA, to place an upper limit for possible Planck-scale modifications on the ground-state energy of an oscillator. Our analysis calls for the development of a satisfactory treatment of multi-particle states in the framework of quantum gravity models.