We report on the demonstration of a high finesse micro-optomechanical system and identify potential applications ranging from optical cooling to weak force detection to massive quantum superpositions. The system consists of a high quality 30μm diameter flat dielectric mirror cut from a larger substrate with a focused ion beam and attached to an atomic force microscope cantilever. Cavity ring-down measurements performed on a 25 mm long Fabry-Pérot cavity with the 30μm mirror at one end show an optical finesse of 2100. Numerical calculations show that the finesse is not diffraction limited and that orders of magnitude higher finesse should be possible. A mechanical quality factor of more than 105 at pressures below 10-3mbar is demonstrated for the cantilever with a mirror attached.