Throughout the history of the Solar System, Earth has been bombarded by interplanetary dust particles (IDPs), which are asteroid and comet fragments of diameter ~1-1,000µm. The IDP flux is believed to be in quasi-steady state: particles created by episodic main belt collisions or cometary fragmentation replace those removed by comminution, dynamical ejection, and planetary or solar impact. Because IDPs are rich in 3He, seafloor sediment 3He concentrations provide a unique means of probing the major events that have affected the IDP flux and its source bodies over geological timescales. Here we report that collisional disruption of the >150-km-diameter asteroid that created the Veritas family 8.3 +/- 0.5Myr ago also produced a transient increase in the flux of interplanetary dust-derived 3He. The increase began at 8.2 +/- 0.1Myr ago, reached a maximum of ~4 times pre-event levels, and dissipated over ~1.5Myr. The terrestrial IDP accretion rate was overwhelmingly dominated by Veritas family fragments during the late Miocene. No other event of this magnitude over the past ~108yr has been deduced from main belt asteroid orbits. One remarkably similar event is present in the 3He record 35Myr ago, but its origin by comet shower or asteroid collision remains uncertain.