Atmospheric airbursts over Russia at Chelyabinsk in 2013 and Tunguska in 1908 provide dramatic examples of hazards posed by near-Earth objects (NEOs). These two events produced 0.5 and 5 Mt of energy, respectively, which dramatically affected surface environments and, in the case of Chelyabinsk, injured humans. Enigmatic natural glasses have been cited as geologic evidence of the threat posed by large airbursts. Libyan Desert Glass (LDG) is a natural glass found in western Egypt that formed ∼29 m.y. ago, however its origin is disputed; the two main formation hypotheses include melting by meteorite impact or melting by a large, 100 Mt–class airburst. High-temperature fusion occurs during both processes, however airbursts do not produce shocked minerals; airbursts generate overpressures at the level of thousands of pascals in the atmosphere, whereas crater-forming impacts generate shockwaves at the level of billions of pascals on the ground. Here we report the presence in LDG of granular zircon grains that are comprised of neoblasts that preserve systematic crystallographic orientation relations that uniquely form during reversion from reidite, a 30 GPa high-pressure ZrSiO4 polymorph, back to zircon. Evidence of former reidite provides the first unequivocal substantiation that LDG was generated during an event that produced high-pressure shock waves; these results thus preclude an origin of LDG by airburst alone. Other glasses of disputed origin that contain zircon with evidence of former reidite, such as Australasian tektites, similarly were also likely made during crater-forming events. Public-policy discussions and planning to mitigate hazards from airbursts caused by NEOs are clearly warranted, but should be cautious about considering LDG or other glasses with evidence of high-pressure shock deformation as products of an airburst. At present, there are no confirmed examples of products from a 100 Mt–class airburst in the geologic record.