We report a Muon Spin Rotation (μSR) study on single crystalline azurite. The measurements revealed clear evidence for long range magnetic order below the Néel temperature at T_N = 1.9 K. The spectra in the magnetically ordered regime were fitted with three different muon sites, which can be related to muons close to Cu²⁺ monomer and dimer ions, respectively. The spontaneous muon spin rotation frequencies revealed the development of a magnetic order parameter. Below 0.4 K, transverse damping data indicated a further change in the local magnetic environment of the Cu²⁺ monomer ions.