One‐dimensional Vlasov simulations show that when an electron beam is suddenly injected into a plasma, a fast‐moving monotonic shock forms during the early stage of the transient plasma response. In the shock, the ions are nearly immobile. The shock appears to be an electrostatic electron‐beam–plasma mode. The shock evolves from an initial positive potential perturbation, which is supported by an ion burst. The steepening of the perturbation into a shock is characterized by an electron‐beam–plasma mode.