Quantum fluctuations of the electromagnetic vacuum produce measurable physical effects such as Casimir forces and the Lamb shift1. They also impose an observable limit—known as the quantum backaction limit—on the lowest temperatures that can be reached using conventional laser cooling techniques2,3. As laser cooling experiments continue to bring massive mechanical systems to unprecedentedly low temperatures4,5, this seemingly fundamental limit is increasingly important in the laboratory6. Fortunately, vacuum fluctuations are not immutable and can be ‘squeezed’, reducing amplitude fluctuations at the expense of phase fluctuations. Here we propose and experimentally demonstrate that squeezed light can be used to cool the motion of a macroscopic mechanical object below the quantum backaction limit. We first cool a microwave cavity optomechanical system using a coherent state of light to within 15 per cent of this limit. We then cool the system to more than two decibels below the quantum backaction limit using a squeezed microwave field generated by a Josephson parametric amplifier. From heterodyne spectroscopy of the mechanical sidebands, we measure a minimum thermal occupancy of 0.19 ± 0.01 phonons. With our technique, even low-frequency mechanical oscillators can in principle be cooled arbitrarily close to the motional ground state, enabling the exploration of quantum physics in larger, more massive systems.