The nearby dwarf spheroidal galaxy Draco, with its high mass to light ratio, is one of the most auspicious targets for indirect dark matter (DM) searches. Annihilation of hypothetical DM particles can result in high-energy γ-rays, e.g., from neutralino annihilation in the supersymmetric framework. A search for a possible DM signal originating from Draco was performed with the MAGIC telescope during 2007. Analysis of the data results in a flux upper limit (2 σ) of 1.1 × 10-11 photons cm-2 s-1 for photon energies above 140 GeV, assuming a pointlike source. A comparison with predictions from supersymmetric models is also given. While our results do not constrain the mSUGRA phase parameter space, a very high flux enhancement can be ruled out.