Memories are stored and consolidated as a result of a dialogue between the hippocampus and cortex during sleep. Neurons active during behavior reactivate in both structures during sleep, in conjunction with characteristic brain oscillations that may form the neural substrate of memory consolidation. In the hippocampus, replay occurs within sharp wave-ripples: short bouts of high-frequency activity in area CA1 caused by excitatory activation from area CA3. In this work, we develop a computational model of ripple generation, motivated by in vivo rat data showing that ripples have a broad frequency distribution, exponential inter-arrival times and yet highly non-variable durations. Our study predicts that ripples are not persistent oscillations but result from a transient network behavior, induced by input from CA3, in which the high frequency synchronous firing of perisomatic interneurons does not depend on the time scale of synaptic inhibition. We found that noise-induced loss of synchrony among CA1 interneurons dynamically constrains individual ripple duration. Our study proposes a novel mechanism of hippocampal ripple generation consistent with a broad range of experimental data, and highlights the role of noise in regulating the duration of input-driven oscillatory spiking in an inhibitory network.