On asteroids, fractures develop due to stresses driven by diurnal temperature variations at spatial scales ranging from sub-millimetres to metres. However, the timescales of such rock fracturing by thermal fatigue are poorly constrained by observations. Here we analyse images of the asteroid (101955) Bennu obtained by the Origins, Spectral Interpretation, Resource Identification and Security-Regolith Explorer (OSIRIS-REx) mission and show that metre-scale fractures on the boulders exposed at the surface have a preferential meridional orientation, consistent with cracking induced by diurnal temperature variations. Using an analytical model of fracture propagation, we suggest that fractures the length of those on Bennu's boulders can be produced in 104-105 years. This is a comparable or shorter timescale than mass movement processes that act to expose fresh surfaces and reorient boulders and any preferential direction signature. We propose that boulder surface fracturing happens rapidly compared with the lifetime in near-Earth space of Bennu and other carbonaceous asteroids. The damage due to this space-weathering process has consequences for the material properties of these asteroids, with implications for the preservation of the primordial signature acquired during the accretional phases in the protoplanetary disk of our solar system.