Self-assembled columnar AlGaN/GaN nanocavities, with an active region of GaN quantum disks embedded in an AlGaN nanocolumn and cladded by top and bottom AlN/GaN Bragg mirrors, were grown. The nanocavity has no cracks or extended defects, due to the relaxation at the Si interface and to the nanocolumn free-surface to volume ratio. The emission from the active region matched the peak reflectivity by tuning the Al content and the GaN disks thickness. Quantum confinement effects that depend on both the disk thickness and the inhomogeneous strain distribution within the disks are clearly observed.