The MACRO detector has been used to perform a search for bursts of neutrinos from Galactic supernovae from October 1989 to February 1992. We did not detect any burst compatible with a stellar core collapse during this interval. With an active mass of 45 tonnes of liquid scintillator, our search extended to over 60% of the stars in the Galaxy. Both the current and planned future capabilities of MACRO to detect supernovae are described