Cycles of fracture and healing in magma are important controls on outgassing time scales and repetitive seismicity at silicic volcanoes. Here, we experimentally drove silicate melts (at 109-1011 Pa·s) to tensile failure, measuring the strength during fracture of the otherwise liquid material. We then took the same melts with parallel contact surfaces and closed the fracture under compressive stress and recorded the evolution of tensile strength of the interface healed for different times. We provide a semi-empirical model for fracture healing time scales useful for volcanic applications. As the time available for healing is increased, strength nonlinearly recovers toward that of unfractured glass. We parameterized the healing kinetics as a three-stage process: (1) relaxation of the compressive stress, (2) fracture surface-surface wetting, and (3) diffusive removal of the interface. During welding of these surfaces in air, we observed that micropores are trapped along the fracture plane, which may inhibit complete healing and provide a textural record of relict fracture planes in volcanic glasses. We conclude that at magmatic conditions, fracture healing is efficient in crystal-poor melts, and it could rapidly seal outgassing pathways over eruptive time scales, contributing to cyclic behavior associated with recurring gas-and-ash explosions and outgassing events.