We report on the observation of collapse and revival of the fringe pattern in a multiple-beam atom interferometer, when the drift time between the beam splitting processes is varied. The atomic beam splitters are realized with laser pulses pumping the atoms into velocity selective dark states. For small drift times, the interference signal shows the sharply peaked Airy function-like pattern characteristic for multiple-beam interference. The fringe pattern collapses for larger drift times due to a recoil phase shift increasing quadratically with the transverse atomic momentum. When the total interaction time reaches an integer multiple of the inverse two-photon recoil energy in frequency units, the original fringe pattern is revived.