The development of solid-state photonic quantum technologies is of great interest for fundamental studies of light-matter interactions and quantum information science. Diamond has turned out to be an attractive material for integrated quantum information processing due to the extraordinary properties of its colour centres enabling e.g. bright single photon emission and spin quantum bits. To control emitted photons and to interconnect distant quantum bits, micro-cavities directly fabricated in the diamond material are desired. However, the production of photonic devices in high-quality diamond has been a challenge so far. Here we present a method to fabricate one- and two-dimensional photonic crystal micro-cavities in single-crystal diamond, yielding quality factors up to 700. Using a post-processing etching technique, we tune the cavity modes into resonance with the zero phonon line of an ensemble of silicon-vacancy centres and measure an intensity enhancement by a factor of 2.8. The controlled coupling to small mode volume photonic crystal cavities paves the way to larger scale photonic quantum devices based on single-crystal diamond.