We find exact solutions of the hydrodynamic equations of a dilute and ultracold atomic Bose-Einstein condensate confined in the cylindric radial direction by a harmonic potential and freely travelling in the longitudinal axial direction. The dynamics of these solutions, which generalize the ones obtained for a purely one-dimensional superfluid in the regime of quasi-condensation, gives rise to a shock-wave front whose period of formation is analytically estimated. We suggest that these shock waves can be experimentally produced by engineering the initial density and phase of an atomic Bose-Einstein condensate.