We report observations of quantum oscillations in single crystals of the high temperature superconductor MgB_2. Three de Haas-van Alphen frequencies are clearly resolved. We propose that two of these come from a single warped Fermi surface tube along the c direction, and that the third arises from cylindrical sections of the in-plane honeycomb network. The corresponding effective masses range from 0.44-0.68m_e. Our results show some differences from the calculated band-structure, and should help define key parameters in the theory of superconductivity for this compound.