Considerable advances made in the development of nanomechanical and nano-optomechanical devices have enabled the observation of quantum effects1, 2, 3, 4, improved sensitivity to minute forces5, 6, and provided avenues to probe fundamental physics at the nanoscale7, 8, 9. Concurrently, solid-state quantum emitters with optically accessible spin degrees of freedom have been pursued in applications ranging from quantum information science10, 11 to nanoscale sensing12. Here, we demonstrate a hybrid nano-optomechanical system composed of a nanodiamond (containing a single nitrogen–vacancy centre) that is levitated in an optical dipole trap. The mechanical state of the diamond is controlled by modulation of the optical trapping potential. We demonstrate the ability to imprint the multi-dimensional mechanical motion of the cavity-free mechanical oscillator into the nitrogen–vacancy centre fluorescence and manipulate the mechanical system's intrinsic spin. This result represents the first step towards a hybrid quantum system based on levitating nanoparticles that simultaneously engages optical, phononic and spin degrees of freedom.