Recent observations of large-scale structures in the Universe demonstrate the existence of large voids, ~20-60 h_0^-1 Mpc in diameter, encircled by dense walls of galaxies (with a Hubble constant H_0=100 h_0 km s^-1 Mpc^-1). Previous calculations of explosions in the early Universe that attempt to model the formation of the voids produced voids of only <~7.5 h_0^-1 Mpc in radius. We study here the formation of voids beginning from the collapse of a Population III object which created a shock wave. We study the evolution of the shock wave that spreads out, driving and compressing matter in front of it, creating a dense shell. The shell eventually becomes gravitationally unstable, fragmenting into objects which collapse, explode and form a new generation of supernovae. This sequence occurs several times, producing the voids. The simulations were run with the present total matter density equal to 10 per cent of the critical density. Our results demonstrate that it is possible to obtain large voids of matter of dimensions ~17-30 Mpc in radius (with h_0=0.5), and shell masses of the order of clusters of galaxies. We also study the anisotropy in the microwave background generated by our explosive model and compare the results with observations made using the COBE satellite (y_Comp<~1.5x10^-5). We find that the observational limits obtained by the COBE satellite imply that the present filling factor (or the fraction of space enclosed by shells) is f_F<~0.12-0.24 in this explosive scenario. Our model predicts that voids have expansion velocities ~100-400 km s^-1. Our model also predicts that the last explosive cycle producing the observed voids occurred at a redshift 0.5<~Z<~3.5.